Question

simplify each of the following expression.
$( \sqrt{5} + \sqrt {2})^{2}$
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Answer 1

Answer:

$( \sqrt{5} + \sqrt{2} ) {}^{2}$

Using the formula of ( a + b) ^ 2

$( \sqrt{5} \: ) {}^{2} + ( \sqrt{2) {}^{2} } + 2( \sqrt{5)} ( \sqrt{2} )$

$5 + 2 + 2 \sqrt{10}$

$7 + 2 \sqrt{10}$

Answer 2

To find the value of :-

$( \sqrt{5} + \sqrt{2} ) ^{2}$

Concept used:-

$(a + b) ^{2} = {a}^{2} + {b}^{2} + 2ab$

Solution:-

$( \sqrt{5} + \sqrt{2} ) ^{2} \\ = (\sqrt{5} )^{2} + ( { \sqrt{2}) }^{2} + 2 \times \sqrt{5} \times \sqrt{2} \\ = 5 + 2 + 2 \sqrt{10} \\ = 7 + 2 \sqrt{10}$