Question

(5-sqrt3) to the power 2​

Answer 1

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Evaluate $\sf {(5 - \sqrt{3} )}^{2}$

$\star\:\:\:\sf\large\underline\blue{Answer:-}$

$\sf {(5 - \sqrt{3} )}^{2}$

$\sf = {(5)}^{2} + { (\sqrt{3} )}^{2} - 2 \times 5 \times \sqrt{3}$

$\sf = 25 + 3 - 10 \sqrt{3}$

$\sf = 28 - 10 \sqrt{3}$

Answer 2

Given:-

${ \sqrt{5 - \sqrt{3} } }^{2}$

Solution :-

By the identity (a2+2ab+b2) we can solve this Question.

${ \sqrt{5 - \sqrt{3} } }^{2} = {a}^{2} - 2ab + {b}^{2} \\ \\ { \sqrt{5 - \sqrt{3} } }^{2} = \sqrt{5 - \sqrt {3} } \times \sqrt{5 + \sqrt{3} } \\ \\ = > {5}^{2} - 2 \times 5 \times \sqrt{3} + \sqrt{ {3}^{2} } \\ \\ = > 25 - 10 \sqrt{3} + 3 \\ \\ = > \bold{ \red{28 - 10 \sqrt{3} }{} }{}$