Simplify the expression: ( 5 + 2 )^2 - Vidyadip

Question

Simplify the expression:
${\left( {\sqrt 5 + \sqrt 2 } \right)^2}$

✓

Answer

${\left( {\sqrt 5 + \sqrt 2 } \right)^2}$
We need to apply the formula ${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2} \ to \ find\ value\ of \ {\left( {\sqrt 5 + \sqrt 2 } \right)^2}$
${\left( {\sqrt 5 + \sqrt 2 } \right)^2} = {\left( {\sqrt 5 } \right)^2} + 2 \times \sqrt 5 \times \sqrt 2 + {\left( {\sqrt 2 } \right)^2}$
$ = 5 + 2\sqrt {10} + 2$
$= 7 + 2\sqrt {10}$
Therefore, on simplifying ${\left( {\sqrt 5 + \sqrt 2 } \right)^2}$ , we get $7 + 2\sqrt {10} $ Therefore, on simplifying ${\left( {\sqrt 5 + \sqrt 2 } \right)^2}$, we get $7 + 2\sqrt {10}$

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