Question

find the value of √(75 - 12 √(21) , the root is under the whole term

Answer 1

$\sqrt{75-12 \sqrt{21} }$
Here $12 \sqrt{21}=2 \sqrt{756}$
making factors of  $2 \sqrt{756}$
$\sqrt{ \sqrt{12} ^{2} + \sqrt{63} ^{2} -2 \sqrt{(12)(63)} }$
using (a-b)^2 identity
$\sqrt{ (\sqrt{12} - \sqrt{63}) ^{2} }$
$\sqrt{12} - \sqrt{63$