Question

trục căn thức ở mẫu rồi rút gọn

Answer 1

a) √8/(√5 - √3)

= 2√2.(√5 + √3)/[(√5 - √3)(√5 + √3)]

= 2√2(√5 + √3)/2

= √10 + √6

b) √[(2 - √3)/(2 + √3)]

= √{(2 - √3)²/[(2 + √3)(2 - √3)]}

= (2 - √3)/(4 - 3)

= 2 - √3

Answer 2

Lời giải:

a. 

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

b.

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