solve this

Question:

$\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}=?$

(a) $\sqrt{2}$

(b) 2

(c) 4

(d) 8

 

Solution:

$\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$

$=\frac{\sqrt{16 \times 2}+\sqrt{16 \times 3}}{\sqrt{4 \times 2}+\sqrt{4 \times 3}}$

$=\frac{4 \sqrt{2}+4 \sqrt{3}}{2 \sqrt{2}+2 \sqrt{3}} \quad[\sqrt{a b}=\sqrt{a} \times \sqrt{b}]$

$=\frac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}$

$=\frac{4}{2}$

$=2$

Hence, the correct answer is option (b).

 

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