Question

If $P=\sqrt{\left(\sqrt{12}\right)+12+\sqrt{(13+2\sqrt{12}))}}-\sqrt{12}$,then find the value of P?

Answer 1

$P=\sqrt{\left(\sqrt{12}\right)+12+\sqrt{13+2\sqrt{12}\left)\right)}}-\sqrt{12}\because 13+2\sqrt{12}=1^2+{\sqrt{12}}^2+2\times 1\times \sqrt{12}=(\sqrt{12}+1{)}^2$
On solving we will get,
$P=\sqrt{\left(\sqrt{12}\right)+12+\sqrt{(\sqrt{12}+1{)}^2}}-\sqrt{12}=\sqrt{\left(\sqrt{12}\right)+12+\sqrt{12}+1}=\sqrt{12}\sqrt{13+2\sqrt{12}}-\sqrt{12}=\sqrt{(\sqrt{12}+1{)}^2}-\sqrt{12}(Again,usintheaboveresult)=\sqrt{12}+1-\sqrt{12}=1$