{"segment":[{"time":9,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u $>, < =$ v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"$\\sqrt{21}-\\sqrt{5}$ _input_ $\\sqrt{20}-\\sqrt{6}$","hint":"X\u00e9t hi\u1ec7u $\\left( \\sqrt{21}-\\sqrt{5} \\right)-\\left( \\sqrt{20}-\\sqrt{6} \\right)$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\left( \\sqrt{21}-\\sqrt{5} \\right)-\\left( \\sqrt{20}-\\sqrt{6} \\right)$<br\/>$\\,=\\left( \\sqrt{21}-\\sqrt{20} \\right)+\\left( \\sqrt{6}-\\sqrt{5} \\right)$<br\/>V\u00ec $\\sqrt{21}>\\sqrt{20}$ v\u00e0 $\\sqrt{6}>\\sqrt{5}$ n\u00ean $\\left( \\sqrt{21}-\\sqrt{20} \\right)+\\left( \\sqrt{6}-\\sqrt{5} \\right)>0$<br\/>V\u1eady $\\sqrt{21}-\\sqrt{5}>\\sqrt{20}-\\sqrt{6}$<br\/><span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 d\u1ea5u $>$<\/span><\/span>"}]}],"id_ques":481},{"time":9,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-1"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $A=\\sqrt{6-2\\sqrt{5}}-\\sqrt{5}$<br\/>\u0110\u00e1p s\u1ed1:$A =\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$","hint":"T\u00e1ch $6=5+1$. Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u r\u1ed3i t\u00ednh.","explain":"<span class='basic_left'> Ta c\u00f3<br\/>$\\begin{align}A&=\\sqrt{6-2\\sqrt{5}}-\\sqrt{5}\\\\&=\\sqrt{(\\sqrt{5})^2-2.\\sqrt{5}.1+1^2}-\\sqrt{5}\\\\&=\\sqrt{{{\\left( \\sqrt{5}-1 \\right)}^{2}}}-\\sqrt{5}\\\\&=\\sqrt{5}-1-\\sqrt{5}\\,\\,(V\u00ec\\,\\,\\sqrt{5}\\,>\\,1).\\\\&=-1\\end{align}$ <br\/>V\u1eady $A= -1$<br\/> <span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $-1$<\/span><br\/><b> L\u01b0u \u00fd:<\/b><br\/>V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|=\\left\\{ \\begin{align} & a\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a\\ge 0 \\\\ & -a\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a<{0} \\\\\\end{align} \\right.$<\/span> "}]}],"id_ques":482},{"time":9,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $A=\\sqrt{9+4\\sqrt{5}}-\\sqrt{5}$<br\/>\u0110\u00e1p s\u1ed1:$A =\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$","hint":"T\u00e1ch $9=4+5$. Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng r\u1ed3i t\u00ednh.","explain":"<span class='basic_left'>Ta c\u00f3 <br\/>$\\begin{align}A&=\\sqrt{9+4\\sqrt{5}}-\\sqrt{5}\\\\&=\\sqrt{2^2+2.2.\\sqrt{5}+(\\sqrt{5})^2}-\\sqrt{5}\\\\&=\\sqrt{{{\\left( 2+\\sqrt{5} \\right)}^{2}}}-\\sqrt{5}\\\\&=|2+\\sqrt{5}|-\\sqrt{5}\\\\&=2+\\sqrt{5}-\\sqrt{5}\\\\&=2\\\\ \\end{align}$<br\/>V\u1eady $ A= 2$ <br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $2.$<\/span><br\/><b> L\u01b0u \u00fd:<\/b><br\/>V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|=\\left\\{ \\begin{align} & a\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a\\ge 0 \\\\ & -a\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a<{0} \\\\\\end{align} \\right.$<\/span>"}]}],"id_ques":483},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c: $A=\\sqrt{{{\\left( \\sqrt{3}-\\sqrt{2} \\right)}^{2}}}+\\sqrt{2}$<br\/>\u0110\u00e1p s\u1ed1: $A=\\sqrt{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}$","hint":"V\u1edbi m\u1ecdi s\u1ed1 a, ta c\u00f3 $\\sqrt{a^2}=|a|=\\left\\{ \\begin{align} & a\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a\\ge {0} \\\\ & -a\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a<{0} \\\\\\end{align} \\right.$.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align}A&=\\sqrt{{{\\left( \\sqrt{3}-\\sqrt{2} \\right)}^{2}}}+\\sqrt{2}\\\\&=\\left| \\sqrt{3}-\\sqrt{2} \\right|+\\sqrt{2}\\\\&=\\sqrt{3}-\\sqrt{2}+\\sqrt{2}\\,(\\text{v\u00ec} \\,\\sqrt{3}-\\sqrt{2}\\,>\\,0 )\\\\&=\\sqrt{3}\\end{align}$<br\/>V\u1eady $A=\\sqrt{3}$ <br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $\\sqrt{3}$<\/span><\/span>"}]}],"id_ques":484},{"time":9,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai2/lv2/img\/2.jpg' \/><\/center> $\\sqrt{10+2\\sqrt{24}}=\\sqrt{3}+\\sqrt{8}$ ","select":["A. \u0110\u00fang","B. Sai"],"hint":"Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c d\u01b0\u1edbi c\u0103n \u1edf v\u1ebf tr\u00e1i v\u1ec1 d\u1ea1ng h\u1eb1ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c $(a+b)^2$, r\u00fat g\u1ecdn v\u1ebf tr\u00e1i r\u1ed3i so s\u00e1nh v\u1edbi v\u1ebf ph\u1ea3i.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{10+2\\sqrt{24}}$$\\,=\\sqrt{(\\sqrt{4})^2+2.\\sqrt{4}.\\sqrt{6}+(\\sqrt{6})^2}$$\\,=\\sqrt{{{\\left( \\sqrt{4}+\\sqrt{6} \\right)}^{2}}}$$\\,=2+\\sqrt{6}\\ne \\sqrt{3}+\\sqrt{8}$<br\/><span class='basic_pink'>Do \u0111\u00f3 kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 Sai<\/span><\/span>","column":2}]}],"id_ques":485},{"time":9,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/daiso/bai2/lv2/img\/2.jpg' \/><\/center> $\\sqrt{6+2\\sqrt{5}}=\\sqrt{5}+1$ ","select":["A. \u0110\u00fang","B. Sai"],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{6+2\\sqrt{5}}$$\\,=\\sqrt{{{\\left( \\sqrt{5} \\right)}^{2}}+2.\\sqrt{5}.1+{{1}^{2}}}$$\\,=\\sqrt{{{\\left( \\sqrt{5}+1 \\right)}^{2}}}$$\\,=\\sqrt{5}+1$<br\/><span class='basic_pink'>Do \u0111\u00f3 kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00fang<\/span><br\/><b>Nh\u1eadn x\u00e9t:<\/b> V\u1edbi b\u00e0i to\u00e1n n\u00e0y ta c\u00f3 th\u1ec3 gi\u1ea3i b\u1eb1ng c\u00e1ch bi\u1ebfn \u0111\u1ed5i v\u1ebf ph\u1ea3i:<br\/>Ta c\u00f3:<br\/>$\\sqrt{5}+1 = \\sqrt{{{\\left( \\sqrt{5}+1 \\right)}^{2}}}$$\\,=\\sqrt{{{\\left( \\sqrt{5} \\right)}^{2}}+2.\\sqrt{5}.1+{{1}^{2}}}$$\\,=\\sqrt{6+2\\sqrt{5}}$<br\/>V\u1eady $\\sqrt{6+2\\sqrt{5}}=\\sqrt{5}+1$","column":2}]}],"id_ques":486},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["4","-4"],["-4","4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ecm $x$ bi\u1ebft: $\\sqrt{16x^4}=64$ <br\/>\u0110\u00e1p s\u1ed1:$\\left[ \\begin{array}{} x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\end{array} \\right.$","hint":"\u0110\u01b0a th\u1eeba s\u1ed1 \u1edf v\u1ebf tr\u00e1i ra ngo\u00e0i d\u1ea5u c\u0103n r\u1ed3i t\u00ecm $x$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{16{{x}^{4}}}=64\\Leftrightarrow 4{{{x}}^{2}}=64$$\\,\\Leftrightarrow {{x}^{2}}=16\\Leftrightarrow x=\\pm 4$<br\/>V\u1eady $x=\\pm 4$ <br\/><span class='basic_pink'>Do \u0111\u00f3 c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $4$ v\u00e0 $-4$<\/span><\/span>"}]}],"id_ques":487},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["-1","2"],["2","-1"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ecm $x$ bi\u1ebft: $\\sqrt{9x^2}=x+4$ (\u0111i\u1ec1u ki\u1ec7n: x\u2265\u22124)<br\/>\u0110\u00e1p \u00e1n:$\\left[ \\begin{array}{} x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ x = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\end{array} \\right.$","hint":"V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|=\\left\\{ \\begin{align} & a\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\, a\\ge 0 \\\\ & -a\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a< 0 \\\\\\end{align} \\right.$.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\sqrt{{9}{{{x}}^{2}}}=x+4$ (\u0111i\u1ec1u ki\u1ec7n: $x \\ge -4$)<br\/>$\\,\\Leftrightarrow 3\\left| x \\right|=x+4$<br\/>$\\,\\Leftrightarrow \\left[ \\begin{aligned} & 3x=x+4 \\\\ & 3x=-x-4 \\\\ \\end{aligned} \\right.$<br\/>$\\,\\Leftrightarrow \\left[ \\begin{aligned} & x=2 \\\\ & x=-1 \\\\ \\end{aligned} \\right.$ (th\u1ecfa m\u00e3n)<br\/>V\u1eady $x=-1;$ $x=2$ <br\/><span class='basic_pink'>Do \u0111\u00f3, c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1$ v\u00e0 $2.$<\/span><\/span>"}]}],"id_ques":488},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ecm $x$ \u0111\u1ec3 $\\sqrt{{{x}^{2}}-12x+36}=x-6$ ","select":["A. $x < 6 $ ","B. $x < -6$ ","C. $x\\ge 6$ ","D. $x\\ge -6$ "],"hint":"V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|=\\left\\{ \\begin{align} & a\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\, a\\ge 0 \\\\ & -a\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a< 0 \\\\\\end{align} \\right.$. ","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$\\sqrt{{{x}^{2}}-12x+36}=\\sqrt{(x-6)^2}$$\\,=|x-6|$$\\,=\\left\\{ \\begin{align} & x-6\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,x\\ge 6 \\\\ & 6 -x\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,x< 6 \\\\\\end{align} \\right.$<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span>","column":2}]}],"id_ques":489},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"T\u00ecm $x$ \u0111\u1ec3 $\\sqrt{1+10x+25{{x}^{2}}}=-1-5x$ ","select":["A. $x< \\dfrac{1}{5}$ ","B. $x < -\\dfrac{1}{5}$ ","C. $x\\ge \\dfrac{1}{5}$ ","D. $x\\ge -\\dfrac{1}{5}$ "],"hint":"V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|=\\left\\{ \\begin{align} & a\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a\\ge 0 \\\\ & -a\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,a< 0 \\\\\\end{align} \\right.$. ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/> $\\sqrt{1+10x+25{{x}^{2}}}=\\sqrt{(1+5x)^2}$$\\,=|1+5x|$$\\,=\\left\\{ \\begin{align} & 1+5x\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,x\\ge -\\dfrac{1}{5} \\\\ & -1-5x\\,\\,\\,\\,\\text{n\u1ebfu}\\,\\,\\,\\,\\,\\,\\,\\,x< -\\dfrac{1}{5} \\\\\\end{align} \\right.$<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span>","column":2}]}],"id_ques":490},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Ph\u01b0\u01a1ng tr\u00ecnh $\\sqrt{(x-1)^2}=3$ c\u00f3 nghi\u1ec7m l\u00e0: ","select":["A. $x= 4$ ","B. $x= -4$ ","C. $x= \\pm 4$ ","D. $x= 4$ ho\u1eb7c $x = -2$ "],"hint":"V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|$ ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/>V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>Ta c\u00f3: <br\/>$\\sqrt{{{\\left( x-1 \\right)}^{2}}}=3$<br\/>$\\,\\Leftrightarrow \\left| x-1 \\right|=3$<br\/>$\\,\\Leftrightarrow \\left[ \\begin{aligned} & x-1=3 \\\\ & x-1=-3 \\\\ \\end{aligned} \\right.$<br\/>$\\,\\Leftrightarrow \\left[ \\begin{aligned} & x=4 \\\\ & x=-2 \\\\ \\end{aligned} \\right.$.<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S= \\{4; -2\\}$<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D <\/span><\/span>","column":2}]}],"id_ques":491},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"\u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a bi\u1ec3u th\u1ee9c $\\sqrt{a^8b^3}$ l\u00e0: ","select":["A. $b \\ge 0$","B. $a < 0$","C. $b \\le0$ ","D. $b=0$"],"hint":"\u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a $\\sqrt{A}$ l\u00e0 $A \\ge0$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{a^8b^3}$ c\u00f3 ngh\u0129a $\\Leftrightarrow a^8b^3\\ge 0$ <br\/> M\u00e0 $ a^8 \\ge 0$ $\\forall a$ n\u00ean $a^8b^3\\ge 0 \\Leftrightarrow b^3\\ge 0\\Leftrightarrow b \\ge 0$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span>","column":2}]}],"id_ques":492},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":" ","type_check":"","ques":" $\\sqrt{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}-2\\sqrt{2}}=\\sqrt{2}-1$ ","hint":"Bi\u1ebfn \u0111\u1ed5i v\u1ebf ph\u1ea3i v\u1ec1 d\u1ea1ng bi\u1ec3u th\u1ee9c trong c\u0103n th\u1ee9c. T\u1eeb \u0111\u00f3 t\u00ecm y\u1ebfu t\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng.","explain":"<span class='basic_left'>V\u00ec $\\sqrt{2}-1>0$ n\u00ean ta c\u00f3: <br\/>$\\sqrt{2}-1=\\sqrt{{{\\left( \\sqrt{2}-1 \\right)}^{2}}}$<br\/>$\\,=\\sqrt{{{\\left( \\sqrt{2} \\right)}^{2}}-2.\\sqrt{2}.1+{{1}^{2}}}$<br\/>$\\,=\\sqrt{3-2\\sqrt{2}}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $3$<\/span><\/span>"}]}],"id_ques":493},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":" ","type_check":"","ques":" $\\sqrt{8-2\\sqrt{15}}$$=\\sqrt{5}-\\sqrt{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}} $ ","hint":"T\u00e1ch $8=3+5$. Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t hi\u1ec7u r\u1ed3i r\u00fat g\u1ecdn.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng $(a +b)^2$<br\/><b>B\u01b0\u1edbc 2:<\/b> V\u1eadn d\u1ee5ng: V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3:<br\/>$\\sqrt{8-2\\sqrt{15}} \\\\=\\sqrt{{{\\left( \\sqrt{5} \\right)}^{2}}-2.\\sqrt{5}.\\sqrt{3}+{{\\left( \\sqrt{3} \\right)}^{2}}}$<br\/>$\\,=\\sqrt{{{\\left( \\sqrt{5}-\\sqrt{3} \\right)}^{2}}}$<br\/>$\\,=\\left| \\sqrt{5}-\\sqrt{3} \\right|$<br\/>$\\,=\\sqrt{5}-\\sqrt{3}$ <br\/>(V\u00ec $\\sqrt{5}>\\sqrt{3}$) <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $3$<\/span><\/span>"}]}],"id_ques":494},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["2"]]],"list":[{"point":5,"width":40,"content":"","type_input":" ","type_check":"","ques":" $\\sqrt{5+2\\sqrt{6}}=\\sqrt{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}+\\sqrt{3} $ ","hint":"T\u00e1ch $6=2+3.$ Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c d\u01b0\u1edbi d\u1ea5u c\u0103n v\u1ec1 d\u1ea1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t t\u1ed5ng r\u1ed3i r\u00fat g\u1ecdn.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> Bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c v\u1ec1 d\u1ea1ng $(a +b)^2$<br\/><b>B\u01b0\u1edbc 2:<\/b> V\u1eadn d\u1ee5ng: V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|$ <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3:<br\/>$\\sqrt{5+2\\sqrt{6}} \\\\ =\\sqrt{{{\\left( \\sqrt{2} \\right)}^{2}}+2.\\sqrt{2}.\\sqrt{3}+{{\\left( \\sqrt{3} \\right)}^{2}}}$<br\/>$\\,=\\sqrt{{{\\left( \\sqrt{2}+\\sqrt{3} \\right)}^{2}}}$<br\/>$\\,=\\left| \\sqrt{2}+\\sqrt{3} \\right|$<br\/>$\\,=\\sqrt{2}+\\sqrt{3}$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $2$<\/span><\/span>"}]}],"id_ques":495},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"T\u00ecm $a$ \u0111\u1ec3 c\u0103n th\u1ee9c $\\sqrt{4-a^2}$ c\u00f3 ngh\u0129a? ","select":["A. $a \\ge 2$","B. $-2 \\le a \\le 2$","C. $a \\le-2$ ho\u1eb7c $a \\ge 2$ "],"hint":"\u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a $\\sqrt{A}$ l\u00e0 A$\\ge 0$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{4-a^2}$ c\u00f3 ngh\u0129a khi ${4-{a}^{2}}\\ge 0 \\\\ \\Leftrightarrow {{a}^{2}}\\le 4 \\\\ \\Leftrightarrow \\left| a \\right|\\le 2 \\\\ \\Leftrightarrow -2\\le a\\le 2$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span>","column":3}]}],"id_ques":496},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"T\u00ecm $a$ \u0111\u1ec3 c\u0103n th\u1ee9c $\\sqrt{a^2-1}$ c\u00f3 ngh\u0129a? ","select":["A. $a \\ge 1$","B. $a \\le -1$","C. $a \\le -1$ ho\u1eb7c $a \\ge 1$ "],"hint":"\u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh c\u1ee7a $\\sqrt{A}$ l\u00e0 $A\\ge0$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$\\sqrt{{{a}^{2}}-1}$ c\u00f3 ngh\u0129a khi ${{a}^{2}}-1\\ge 0 \\\\ \\Leftrightarrow {{a}^{2}}\\ge 1 \\\\ \\Leftrightarrow \\left| a \\right|\\ge 1$<br\/> $\\Leftrightarrow a\\ge 1$ ho\u1eb7c $a\\le-1$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span><\/span>","column":3}]}],"id_ques":497},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"T\u00ecm $x$ \u0111\u1ec3 c\u0103n th\u1ee9c $\\sqrt{\\dfrac{2}{{{x}^{2}}}}$ c\u00f3 ngh\u0129a? ","select":["A. $x\\ne0$","B. $x\\ge0$","C. $0\\le x < 2$ ","D. $x <0$ "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$\\sqrt{\\dfrac{2}{{{x}^{2}}}}$ c\u00f3 ngh\u0129a khi $ \\dfrac{2}{{{x}^{2}}}\\ge 0\\Leftrightarrow x\\ne 0$ <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span><\/span>","column":2}]}],"id_ques":498},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["2,5"]]],"list":[{"point":5,"width":40,"content":"","type_input":" ","type_check":"","ques":" $3.\\sqrt{{{\\left( -1,5 \\right)}^{2}}}-4.\\sqrt{{{\\left( -0,5 \\right)}^{2}}}$$\\,=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$<br\/>(Vi\u1ebft k\u1ebft qu\u1ea3 d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n)","hint":"V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$3.\\sqrt{{{\\left( -1,5 \\right)}^{2}}}-4.\\sqrt{{{\\left( -0,5 \\right)}^{2}}} \\\\ =3.\\left| -1,5 \\right|-4. |0,5| \\\\ =4,5-2 \\\\=2,5$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $2,5$<\/span><\/span>"}]}],"id_ques":499},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["128"]]],"list":[{"point":5,"width":40,"content":"","type_input":"T\u00ednh ","type_check":"","ques":" $4\\sqrt{{{\\left( -3 \\right)}^{6}}}+5\\sqrt{{{\\left( -2 \\right)}^{4}}}=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ ","hint":"V\u1edbi m\u1ecdi s\u1ed1 $a$, ta c\u00f3 $\\sqrt{a^2}=|a|$","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$4\\sqrt{{{\\left( -3 \\right)}^{6}}}+5\\sqrt{{{\\left( -2 \\right)}^{4}}}$$\\,=4.\\left| {{\\left( -3 \\right)}^{3}} \\right|+5\\left| {{\\left( -2 \\right)}^{2}} \\right|$$\\,=4.27+5.4=128$ <br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $128$<\/span><\/span>"}]}],"id_ques":500}],"lesson":{"save":0,"level":2}}