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`(a+4 sqrt a +4)/(sqrt a+2)`

`= (sqrt a+2)^2/(sqrt a+2)`

`= sqrt a +2`

\(=\dfrac{\left(\sqrt{a}+2\right)^2}{\sqrt{a}+2}=\sqrt{a}+2\)

22 tháng 7 2023

\(8.\dfrac{\sqrt{3}}{\sqrt{2}}=8.\dfrac{\sqrt{3}.\sqrt{2}}{\sqrt{2}.\sqrt{2}}=8.\dfrac{\sqrt{6}}{2}=4\sqrt{6}\)

\(\dfrac{\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{6}}{2}\)

`(a+b-2sqrt(ab))/(sqrt a-sqrtb)`

`= (sqrta-sqrtb)^2/(sqrta-sqrtb)`

`= sqrt a- sqrt b`

`(1+a sqrt a)/(1 + sqrt a)`

`= ((1+sqrta)(1-sqrta+a))/(1+sqrta)`

`= a - sqrt a +1`

AH
Akai Haruma
Giáo viên
19 tháng 7 2021

Bài 1:
a.

\(\frac{1}{2\sqrt{2}-3\sqrt{3}}=\frac{2\sqrt{2}+3\sqrt{3}}{(2\sqrt{2}-3\sqrt{3})(2\sqrt{2}+3\sqrt{3})}=\frac{2\sqrt{2}+3\sqrt{3}}{(2\sqrt{2})^2-(3\sqrt{3})^2}=\frac{2\sqrt{2}+3\sqrt{3}}{-19}\)

b.

\(=\sqrt{\frac{(3-\sqrt{5})^2}{(3-\sqrt{5})(3+\sqrt{5})}}=\sqrt{\frac{(3-\sqrt{5})^2}{3^2-5}}=\sqrt{\frac{(3-\sqrt{5})^2}{4}}=\sqrt{(\frac{3-\sqrt{5}}{2})^2}=|\frac{3-\sqrt{5}}{2}|=\frac{3-\sqrt{5}}{2}\)

 

AH
Akai Haruma
Giáo viên
19 tháng 7 2021

Bài 2.

a. 

\(=\frac{\sqrt{8}(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}=\frac{2\sqrt{2}(\sqrt{5}+\sqrt{3})}{5-3}=\sqrt{2}(\sqrt{5}+\sqrt{3})=\sqrt{10}+\sqrt{6}\)

b.

\(=\sqrt{\frac{(2-\sqrt{3})^2}{(2-\sqrt{3})(2+\sqrt{3})}}=\sqrt{\frac{(2-\sqrt{3})^2}{2^2-3}}=\sqrt{(2-\sqrt{3})^2}=|2-\sqrt{3}|=2-\sqrt{3}\)

a: \(\dfrac{6}{5\sqrt{8}}=\dfrac{6}{10\sqrt{2}}=\dfrac{3}{5\sqrt{2}}=\dfrac{3\sqrt{2}}{10}\)

b: \(\dfrac{7}{5+2\sqrt{3}}=\dfrac{7\left(5-2\sqrt{3}\right)}{13}\)

c: \(\dfrac{6}{\sqrt{7}-\sqrt{5}}=\dfrac{6\left(\sqrt{7}+\sqrt{5}\right)}{2}=3\left(\sqrt{7}+\sqrt{5}\right)\)

24 tháng 8 2023

a) \(\dfrac{6}{5\sqrt{8}}\)

\(=\dfrac{6}{5\cdot2\sqrt{2}}\)

\(=\dfrac{6}{10\sqrt{2}}\)

\(=\dfrac{3\sqrt{2}}{5\sqrt{2}\cdot\sqrt{2}}\)

\(=\dfrac{3\sqrt{2}}{10}\)

b) \(\dfrac{7}{5+2\sqrt{3}}\)

\(=\dfrac{7\left(5-2\sqrt{3}\right)}{\left(5+2\sqrt{3}\right)\left(5-2\sqrt{3}\right)}\)

\(=\dfrac{7\left(5-2\sqrt{3}\right)}{5^2-\left(2\sqrt{3}\right)^2}\)

\(=\dfrac{7\left(5-2\sqrt{3}\right)}{13}\)

\(=\dfrac{35-14\sqrt{3}}{13}\)

c) \(\dfrac{6}{\sqrt{7}-\sqrt{5}}\)

\(=\dfrac{6\left(\sqrt{7}+\sqrt{5}\right)}{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)}\)

\(=\dfrac{6\left(\sqrt{7}+\sqrt{5}\right)}{2}\)

\(=3\sqrt{7}+3\sqrt{5}\)

7 tháng 8 2018

\(A=\frac{1}{\sqrt[3]{9}-\sqrt[3]{3}+\sqrt[3]{24}-\sqrt[3]{243}+\sqrt[3]{375}}\)

\(=\frac{1}{\sqrt[3]{9}-\sqrt[3]{3}+\sqrt[3]{8.3}-\sqrt[3]{27.9}+\sqrt[3]{125.3}}\)

\(=\frac{1}{\sqrt[3]{9}-\sqrt[3]{3}+2\sqrt[3]{3}-3\sqrt[3]{9}+5\sqrt[3]{3}}\)

\(=\frac{1}{6\sqrt[3]{3}-2\sqrt[3]{9}}=\frac{1}{2\sqrt[3]{9}.\left(\sqrt[3]{9}-1\right)}\)

\(=\frac{\sqrt[3]{81}.\left(\sqrt[3]{81}+\sqrt[3]{9}+1\right)}{2\sqrt[3]{9}.\left(\sqrt[3]{9}-1\right)\left(\sqrt[3]{81}+\sqrt[3]{9}+1\right).\sqrt[3]{81}}\)

\(=\frac{9\sqrt[3]{9}+9+3\sqrt[3]{3}}{144}\)

p/s: mk k chắc, sai đâu mn ib cho mk nhé

9 tháng 8 2018

thank bạn nhiều nha

8 tháng 8 2023

\(\dfrac{1}{\sqrt{a}-1}\)

\(=\dfrac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)

\(=\dfrac{\sqrt{a}+1}{\left(\sqrt{a}\right)^2-1^2}\)

\(=\dfrac{\sqrt{a}+1}{a-1}\)

3 tháng 8 2016

\(\frac{1}{\sqrt{3}+\sqrt{2}+1}=\frac{\sqrt{3}+\sqrt{2}-1}{\left(\sqrt{3}+\sqrt{2}\right)^2-1}=\frac{\sqrt{3}+\sqrt{2}-1}{4+2\sqrt{6}}=\frac{\left(\sqrt{3}+\sqrt{2}-1\right)\left(2\sqrt{6}-4\right)}{2^2.6-4^2}=\frac{........}{8}\)

2 tháng 12 2019