Question

√[(√3+1)/(√3-1)]
Please answer it's very urgent.

Answer 1

Answer:

$\mathtt\purple{❖Question:-}$

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

$\mathtt\purple{❖Concept \: used:-}$

Rationalising denominator

$\mathtt\purple{❖Formula \: used:-}$

$\mathtt{ {(a - b)(a - b) = (a - b)}^{2} }$

$\mathtt{(a + b)(a - b) = {a}^{2} - {b}^{2} }$

$\mathtt\purple{❖Solution:-}$

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

$\mathtt{ = \frac{( \sqrt{3})^{2} + 2 \times \sqrt{3} \times 1 + {1}^{2} }{ (\sqrt{3})^{2} - {1}^{2} } }$

$\mathtt{ = \frac{3 + 2 \sqrt{3} + 1 }{3 - 1} }$

$\mathtt{ = \frac{4+ 2 \sqrt{3} }{2} }$

Take 2 common

$\mathtt{ = \frac{2(2 + \sqrt{3)} }{2} }$

$\mathtt{ = \frac{2 + \sqrt{3} }{1} }$

Step-by-step explanation:

I hope this helps you mate.

Answer 2

Step-by-step explanation:

hope it may help you #666