Trục căn thức ở mẫu các biểu thức sau:
\(a,\frac{2\sqrt{10}-5}{4-\sqrt{10}}\)
\(b,\frac{9-2\sqrt{2}}{3\sqrt{6}-2\sqrt{2}}\)
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2 tháng 7 2019
\(a,\frac{\sqrt{5}}{\sqrt{3-\sqrt{5}}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{\left(3-\sqrt{5}\right).\left(3+\sqrt{5}\right)}}\)
\(=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{9-5}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{\sqrt{4}}=\frac{\sqrt{5}\left(\sqrt{3+\sqrt{5}}\right)}{2}\)
27 tháng 9 2016
a. \(\frac{26}{5-2\sqrt{3}}\)=\(\frac{26\cdot\left(5+2\sqrt{3}\right)}{\left(5-2\sqrt{3}\right)\left(5+2\sqrt{3}\right)}\)=\(\frac{26\cdot\left(5+2\sqrt{3}\right)}{5^2-\left(2\sqrt{3}\right)^2}=\frac{26\cdot\left(5+2\sqrt{3}\right)}{13}=2\cdot\left(5+2\sqrt{3}\right)=10+4\sqrt{3}\)
b.\(\frac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}=\frac{\sqrt{3}\cdot\left(3\sqrt{3}-2\right)}{\sqrt{2}\cdot\left(3\sqrt{3}-2\right)}=\frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{6}}{2}\)
c.\(\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{\sqrt{5}\cdot\left(2\sqrt{2}-\sqrt{5}\right)}{\sqrt{2}\cdot\left(2\sqrt{2}-\sqrt{5}\right)}=\frac{\sqrt{5}}{\sqrt{2}}=\frac{\sqrt{10}}{2}\)
d.\(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}\)=\(4\sqrt{5}\)
3 tháng 8 2020
a/ \(\frac{1}{2+\sqrt{3}}-\frac{1}{2-\sqrt{3}}+5\sqrt{3}\)
\(=\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}-\frac{2+\sqrt{3}}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}+5\sqrt{3}\)
\(=\frac{2-\sqrt{3}}{4-3}-\frac{2+\sqrt{3}}{4-3}+5\sqrt{3}\)
\(=2-\sqrt{3}-2-\sqrt{3}+5\sqrt{3}\)
\(=3\sqrt{3}\)
Vậy..
3 tháng 8 2020
b/ \(\frac{1}{\sqrt{5}+2}-\sqrt{9+4\sqrt{5}}\)
\(=\frac{1}{\sqrt{5}+2}-\sqrt{\left(\sqrt{5}+2\right)^2}\)
\(=\frac{1}{\sqrt{5}+2}-\left|\sqrt{5}+2\right|\)
\(=\frac{\sqrt{5}-2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}-\sqrt{5}-2\)
\(=\sqrt{5}-2-\sqrt{5}-2\)
\(=-4\)
Vậy..
A
4 tháng 9 2020
Bài 1 :
a, \(\frac{2ab}{\sqrt{a}+\sqrt{b}}=\frac{2ab\left(\sqrt{a}-\sqrt{b}\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}=\frac{2ab\left(\sqrt{a}-\sqrt{b}\right)}{a-b}\)
b, \(\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{\left(2\sqrt{10}-5\right)\left(4+\sqrt{10}\right)}{\left(4-\sqrt{10}\right)\left(4+\sqrt{10}\right)}=\frac{\sqrt{10}}{2}\)
c, \(\frac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}=\frac{\left(9-2\sqrt{3}\right)\left(3\sqrt{6}+2\sqrt{2}\right)}{\left(3\sqrt{6}-2\sqrt{2}\right)\left(3\sqrt{6}+2\sqrt{2}\right)}=\frac{\sqrt{6}}{2}\)
NN
4 tháng 9 2020
2. \(\frac{1}{\sqrt{3}-\sqrt{2}}-\frac{2}{\sqrt{7}+\sqrt{5}}-\frac{3}{\sqrt{7-2\sqrt{10}}}+\frac{4}{\sqrt{10+2\sqrt{21}}}\)
\(=\frac{\sqrt{3}+\sqrt{2}}{3-2}-\frac{2.\left(\sqrt{7}-\sqrt{5}\right)}{7-5}-\frac{3}{\sqrt{2-2\sqrt{10}+5}}+\frac{4}{\sqrt{3+2\sqrt{21}+7}}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)-\frac{2\left(\sqrt{7}-\sqrt{5}\right)}{2}-\frac{3}{\sqrt{\left(\sqrt{2}-\sqrt{5}\right)^2}}+\frac{4}{\sqrt{\left(\sqrt{3}+\sqrt{7}\right)^2}}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)-\left(\sqrt{7}-\sqrt{5}\right)-\frac{3}{\left|\sqrt{2}-\sqrt{5}\right|}+\frac{4}{\left|\sqrt{3}+\sqrt{7}\right|}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)-\left(\sqrt{7}-\sqrt{5}\right)-\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{3}+\sqrt{7}}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)-\left(\sqrt{7}-\sqrt{5}\right)-\frac{3.\left(\sqrt{5}+\sqrt{2}\right)}{5-2}+\frac{4.\left(\sqrt{7}-\sqrt{3}\right)}{7-3}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)-\left(\sqrt{7}-\sqrt{5}\right)-\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{3}+\frac{4\left(\sqrt{7}-\sqrt{3}\right)}{4}\)
\(=\left(\sqrt{3}+\sqrt{2}\right)-\left(\sqrt{7}-\sqrt{5}\right)-\left(\sqrt{5}+\sqrt{2}\right)+\left(\sqrt{7}-\sqrt{3}\right)\)
\(=\sqrt{3}+\sqrt{2}-\sqrt{7}+\sqrt{5}-\sqrt{5}-\sqrt{2}+\sqrt{7}-\sqrt{3}=0\)
24 tháng 4 2021
+ Ta có:
2√6−√5=2(√6+√5)(√6−√5)(√6+√5)26−5=2(6+5)(6−5)(6+5)
=2(√6+√5)(√6)2−(√5)2=2(√6+√5)6−5=2(6+5)(6)2−(5)2=2(6+5)6−5
=2(√6+√5)1=2(√6+√5)=2(6+5)1=2(6+5).
+ Ta có:
3√10+√7=3(√10−√7)(√10+√7)(√10−√7)310+7=3(10−7)(10+7)(10−7)
=3(√10−√7)(√10)2−(√7)2=3(10−7)(10)2−(7)2=3(√10−√7)10−7=3(10−7)10−7
=3(√10−√7)3=√10−√7=3(10−7)3=10−7.
+ Ta có:
1√x−√y=1.(√x+√y)(√x−√y)(√x+√y)1x−y=1.(x+y)(x−y)(x+y)
=√x+√y(√x)2−(√y)2=√x+√yx−y=x+y(x)2−(y)2=x+yx−y
+ Ta có:
2ab√a−√b=2ab(√a+√b)(√a−√b)(√a+√b)2aba−b=2ab(a+b)(a−b)(a+b)
=2ab(√a+√b)(√a)2−(√b)2=2ab(√a+√b)a−b=2ab(a+b)(a)2−(b)2=2ab(a+b)a−b.
24 tháng 4 2021
\(\frac{2}{\sqrt{6}-\sqrt{5}}=\frac{2\left(\sqrt{6}+\sqrt{5}\right)}{\left(\sqrt{6}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}\right)}=\frac{2\left(\sqrt{6}+\sqrt{5}\right)}{6-5}=2\left(\sqrt{6}+\sqrt{5}\right)\)
\(\frac{3}{\sqrt{10}+\sqrt{7}}=\frac{3\left(\sqrt{10}-\sqrt{7}\right)}{\left(\sqrt{10}-\sqrt{7}\right)\left(\sqrt{10}+\sqrt{7}\right)}=\frac{3\left(\sqrt{10}-\sqrt{7}\right)}{10-7}=\sqrt{10}-\sqrt{7}\)
\(\frac{1}{\sqrt{x}-\sqrt{y}}=\frac{\sqrt{x}+\sqrt{y}}{x-y}\)
\(\frac{2ab}{\sqrt{a}-\sqrt{b}}=\frac{2ab\left(\sqrt{a}+\sqrt{b}\right)}{a-b}\)
\(a,\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{\left(2\sqrt{10}-5\right)\left(4+\sqrt{10}\right)}{\left(4-\sqrt{10}\right)\left(4+\sqrt{10}\right)}=\frac{20+6\sqrt{10}-5\sqrt{10}-9}{16-10}.\)
\(=\frac{11-\sqrt{10}}{6}\)
\(b,=\frac{\left(9-2\sqrt{2}\right)\left(3\sqrt{6}+2\sqrt{2}\right)}{\left(3\sqrt{6}-2\sqrt{2}\right)\left(3\sqrt{6}+2\sqrt{2}\right)}=\frac{\left(9-2\sqrt{2}\right)\left(3\sqrt{6}+2\sqrt{2}\right)}{54-8}\)
\(=\frac{\left(9-2\sqrt{2}\right)\left(3\sqrt{6}+2\sqrt{2}\right)}{46}\)