Question

√{ (√3-1)
(√3+1) }
please write step by step

Answer 1

Answer:

The answer is $\frac{\sqrt 6-\sqrt 2}{2}$

Step-by-step explanation:

 $\sqrt{\frac{\sqrt 3-1}{\sqrt 3+1}\times \frac{\sqrt 3-1}{\sqrt 3-1}}$

$=\sqrt{\frac{(\sqrt 3-1)^2}{(\sqrt 3)^2-1^2}}$, using $(a-b)(a+b)=a^2-b^2$

$=\sqrt{\frac{(\sqrt 3-1)^2}{3-1}}=\sqrt{\frac{(\sqrt 3-1)^2}{2}}\\=\frac{\sqrt{(\sqrt 3-1)^2}}{\sqrt 2}=\frac{\sqrt 3-1}{\sqrt 2}\\=\frac{\sqrt 3-1}{\sqrt 2}\times \frac{\sqrt 2}{\sqrt 2}=\frac{\sqrt 6-\sqrt 2}{2}$, since $(\sqrt a)^2=a$