Question

simplify (underoot3+underroot11)²+(underroot3-underoot11)²​

Answer 1

To Simplify :

$\sf{ (\sqrt{3} + \sqrt{11})^2 + ( \sqrt{3} - \sqrt{11}^2)}$

Explanation :

As, we have to simplify the above given number. So, we will do this question by using some identities.

$\large{\underline{\star{\boxed{\sf{ (a + b)^2 = a^2 + b^2 + 2ab}}}}}$

$\large{\underline{\star{\boxed{\sf{ (a - b)^2 = a^2 + b^2 - 2ab}}}}}$

Putting values

$\sf{\dashrightarrow \bigg( (\sqrt{3}^2) + (\sqrt{11}^2) + 2(\sqrt{3})(\sqrt{11}) \bigg) + \bigg( (\sqrt{3}^2) + (\sqrt{11}^2) -2(\sqrt{3})(\sqrt{11}) \bigg)} \\ \\ \sf{\dashrightarrow \bigg(3 + 11 \cancel{+ 2\sqrt{33}} \bigg) + \bigg( 3 + 11\cancel{ - 2\sqrt{33}} \bigg)} \\ \\ \sf{\dashrightarrow 3 + 11 + 3 + 11} \\ \\ \sf{\dashrightarrow 28} \\ \\ \large{\star{\underline{\boxed{\sf{28}}}}}$

$\mathbb{HENCE \: SIMPLIFIED}$