Bài 8: Rút gọn biểu thức chứa căn bậc hai
Các câu hỏi tương tự
rút gọn biểu thức:
1/ frac{sqrt{15}-sqrt{5}}{sqrt{3}-1}+frac{5-2sqrt{5}}{2sqrt{5}-4}
2/ frac{sqrt{15}-sqrt{12}}{sqrt{5}-2}+frac{6+2sqrt{6}}{sqrt{3}+sqrt{2}}
3/ frac{3+2sqrt{3}}{sqrt{3}}+frac{2+sqrt{2}}{sqrt{2}+1}-left(2+sqrt{3}right)
4/ left(1-frac{5+sqrt{5}}{1+sqrt{5}}right)left(frac{5-sqrt{5}}{1-sqrt{5}}-1right)
giúp minh với cần gấp lắm
Đọc tiếp
rút gọn biểu thức:
1/ \(\frac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\frac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
2/ \(\frac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}+\frac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
3/ \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{\sqrt{2}+1}-\left(2+\sqrt{3}\right)\)
4/ \(\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
giúp minh với cần gấp lắm
Rút gọn biểu thức:
a,\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)
b,\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
c,\(\left(1+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right).\left(1-\frac{a+2\sqrt{a}}{2+\sqrt{a}}\right)\)
Giúp mk vs,mk cần gấp
1. Rút gọn
D = \(\frac{\sqrt{1+\frac{2\sqrt{2}}{3}}+\sqrt{1-\frac{2\sqrt{2}}{3}}}{\sqrt{1+\frac{2\sqrt{2}}{3}}-\sqrt{1-\frac{2\sqrt{2}}{3}}}\)
2. Chứng minh rằng:
\(\frac{a\sqrt{b}+b}{a-b}.\sqrt{\frac{ab+b^2-2\sqrt{ab^3}}{a\left(a+2\sqrt{b}\right)+b}}\left(\sqrt{a}+\sqrt{b}\right)=b\) với ( a > b > 0 )
1 .
a)Afrac{2}{2sqrt[3]{2}+2+sqrt[3]{4}}
b)Bfrac{6}{2sqrt[3]{2}-2+sqrt[3]{4}}
c)Cfrac{2}{sqrt[3]{4}+sqrt[3]{2}+2}
2 .
a)Asqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
b)Bfrac{left(5+2sqrt{6}right).left(49-20sqrt{6}right).sqrt{5-2sqrt{6}}}{9sqrt{3}-11sqrt{2}}
c)Csqrt{4+sqrt{5sqrt{3}+5sqrt{48-10sqrt{7}+4sqrt{3}}}}
d)D(left(sqrt{3}-1right).sqrt{6+2sqrt{2}.sqrt{3-sqrt{sqrt{2}+sqrt{12}+sqrt{18-sqrt{128}}}}}
Đọc tiếp
1 .
a)\(A=\frac{2}{2\sqrt[3]{2}+2+\sqrt[3]{4}}\)
b)\(B=\frac{6}{2\sqrt[3]{2}-2+\sqrt[3]{4}}\)
c)C=\(\frac{2}{\sqrt[3]{4}+\sqrt[3]{2}+2}\)
2 .
a)\(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
b)\(B=\frac{\left(5+2\sqrt{6}\right).\left(49-20\sqrt{6}\right).\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
c)C=\(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7}+4\sqrt{3}}}}\)
d)D=(\(\left(\sqrt{3}-1\right).\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12}+\sqrt{18-\sqrt{128}}}}}\)
Rút gọn các biểu thức sau: 9, A sqrt{4+sqrt{15}}-sqrt{7-3sqrt{5}}10, A sqrt{2+sqrt{3}}+sqrt{2-sqrt{3}}11, A text{}text{}text{}sqrt{12-3sqrt{7}}-sqrt{12+3sqrt{7}}12, A left(3sqrt{2}+sqrt{6}right)sqrt{6-3sqrt{3}}13, A sqrt{9-4sqrt{5}}-sqrt{14-6sqrt{5}}
Đọc tiếp
Rút gọn các biểu thức sau:
9, A = \(\sqrt{4+\sqrt{15}}-\sqrt{7-3\sqrt{5}}\)
10, A = \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
11, A = \(\text{}\text{}\text{}\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)
12, A = \(\left(3\sqrt{2}+\sqrt{6}\right)\sqrt{6-3\sqrt{3}}\)
13, A = \(\sqrt{9-4\sqrt{5}}-\sqrt{14-6\sqrt{5}}\)
* rút gọn biểu thức:
a, sqrt{frac{3}{20}}+sqrt{frac{1}{60}}-2sqrt{frac{1}{15}}
b, left(frac{1}{sqrt{5}-sqrt{3}}+frac{1}{sqrt{5}+sqrt{3}}right).sqrt{5}
c, left(5sqrt{3}+3sqrt{5}right):sqrt{15}
d, left(2+sqrt{5}right)^2-left(2+sqrt{5}right)^2
e, frac{1}{3}sqrt{48}+3sqrt{75}-sqrt{27}-10sqrt{1frac{1}{3}}
Đọc tiếp
* rút gọn biểu thức:
a, \(\sqrt{\frac{3}{20}}+\sqrt{\frac{1}{60}}-2\sqrt{\frac{1}{15}}\)
b, \(\left(\frac{1}{\sqrt{5}-\sqrt{3}}+\frac{1}{\sqrt{5}+\sqrt{3}}\right).\sqrt{5}\)
c, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
d, \(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)
e, \(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\frac{1}{3}}\)
B1. Tính giá trị của các biểu thức sau
a) M= \(\sqrt{4-\sqrt{10-2\sqrt{5}}}-\sqrt{4+\sqrt{10-2\sqrt{5}}}\)
b) P= \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
c) Q= \(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
Rút gọn: \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2}+\sqrt{3}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2}-\sqrt{3}}\)
rút gọn biểu thức sau
\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)