Given: 6√(36)+5√(12)=6 nbsp;× nbsp;6+5√(4 nbsp;× nbsp;3) nbsp; [∵√(36)=6]=36+5×√(4)×√(3) nbsp; nbsp;[∵ √(ab)=√(a)×√(b)]=36+5× 2×√(3) nbsp ...

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Identities for Irrational Numbers

Simplify: 6√(...

Question

Simplify: $6 \sqrt{36} + 5 \sqrt{12}$

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Solution

Given: $6 \sqrt{36} + 5 \sqrt{12}$
$= 6 \times 6 + 5 \sqrt{4 \times 3}$ [ $∵ \sqrt{36} = 6$ ]
$= 36 + 5 \times \sqrt{4} \times \sqrt{3}$ [ $∵$ $\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ ]
$= 36 + 5 \times 2 \times \sqrt{3}$ [ $∵ \sqrt{4} = 2$ ]
$= 36 + 10 \sqrt{3}$
Therefore, $6 \sqrt{36} + 5 \sqrt{12} = 36 + 10 \sqrt{3}$

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