Question

If ,

$\sqrt{a} = \sqrt{108} - \sqrt{363} + \sqrt{192} - \sqrt{12}$
find a

Answer 1

$<h2><font color = red > hey there$



$\sqrt{108} - \sqrt{363} + \sqrt{192} - \sqrt{12}$



$6 \sqrt{3 } - 11 \sqrt{3} + 8 \sqrt{3} - 2 \sqrt{3}$



$- 5 \sqrt{3} + 6 \sqrt{3}$



$\sqrt{ a} = \sqrt{3}$


a=3


Hope it helps you

Thanks for asking....


@Prabhudutt

Answer 2

$\huge{Solution:-}$


$\sqrt{a} = \sqrt{108} - \sqrt{363} + \sqrt{192} - \sqrt{12}$


$\textbf{Simplify the radical}$


$= > \sqrt{a} = 6 \sqrt{3} - 11 \sqrt{3} + 8 \sqrt{3} - 2 \sqrt{3} \\ \\ = > \sqrt{a} = \sqrt{3} \\ \\ square \: \: both \: \: sides \\ \\ = > a = 3 \\ \\ check \: \: if \: \: the \: \: given \: \: value \\ \: \: is \: \: the \: \: solution \: \: of \: \: the \\ \: \: equation$

$= > \sqrt{3} = \sqrt{108} - \sqrt{363} + \sqrt{192} - \sqrt{12} \\ \\ simplify \: \: the \: \: equality \: \: \\ \\ = > 1.73205 = 1.73205 \\ \\ the \: \: equality \: \: is \: \: true \: \: a = 3 \\ \: \: is \: \: a \: \: solution \: \: of \: \: the \: \: equation \\ \\ = > a = 3.$


Hope it helps!