Question

find squar root of
$14 + 6 \sqrt{5}$
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Answer 1

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To Solve:

• find squar root of 14 + 6√5

Solⁿ:

14 + 6√5

$= 9 + 5 + 6 \sqrt{5} \: \: (splitting \: \: 14 \: \: as \: \: 9 + 5)$

Now, 9 is 3²

$= {3}^{2} + { \sqrt{5} }^{2} + 6 \sqrt{5}$

$= {3}^{2} +6 \sqrt{5} + \sqrt{5}$

Now, 6 is 2×3

$= {3}^{2} + 2 \times 3 \times \sqrt{5} +{ \sqrt{5} }^{2}$

Applying the Identity: (a+b)² = a² + b² + 2ab

So,

$14 + 6 \sqrt{5} = \sqrt{{ (3 + \sqrt{5})}^{2}}$

$Square \: \: root \: \: of \: \: 14 + 6 \sqrt{5} = 3 + \sqrt{5}$

HOPE IT WAS USEFUL~