Question

Find the square root of
$24 + 4\sqrt {15} - 4\sqrt {21} - 2\sqrt {35} $

Answer 1

Hint: We have to simplify the equation to make it a perfect square and then find its square root.

Complete step-by-step answer:
We have the given equation $24 + 4\sqrt {15} - 4\sqrt {21} - 2\sqrt {35} $
So hence on doing simplification we have,
$ = 24 + 2\sqrt 5 \times 2\sqrt 3 - 2\sqrt 7 \times 2\sqrt 3 - 2\sqrt 5 \times \sqrt 7 $
$ = 5 + 7 + 12 + 2\sqrt 5 \times 2\sqrt 3 - 2\sqrt 7 \times 2\sqrt 3 - 2\sqrt 5 \times \sqrt 7 $
So if you look carefully, it is in the form of ${\left( {a + b + c} \right)^2} = {a^2} + {b^2} + {c^2} + 2\left( {ab + bc + ca} \right)$
Therefore we will get,
$ = {\left( {\sqrt 5 + 2\sqrt 3 - \sqrt 7 } \right)^2}$
And hence square root of $24 + 4\sqrt {15} - 4\sqrt {21} - 2\sqrt {35} $
$ \pm {\left( {\sqrt 5 + 2\sqrt 3 - \sqrt 7 } \right)^2}$

Note: In this type of question where we have to find the square root, first of all we’ll simplify the given equation and try to make the perfect square. When a square root is found, people often tend to miss the negative roots, so try to not make such mistakes.