Question

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

Answer 1

Step-by-step explanation:

(√32+√48)/(√8+√12)

(2√8+2√12)/(√8+√12)

{2(√8+√12)}/(√8+√12)

2

Answer 2

Answer:

2

Step-by-step explanation:

$\frac{\sqrt{32} +\sqrt{48} }{\sqrt{8}+\sqrt{12} } \\= \frac{\sqrt{32+48} }{\sqrt{8+12} } \\= \frac{\sqrt{80} }{\sqrt{20} }$Prime Factorize 80 and 20

80 = 2 x 2 x 2 x 2 x 5

20 = 2 x 2 x 5

Pair up the like values and bring out of square root

√80 = 2 x 2√5

√20 = 2√5

$\frac{4\sqrt{5} }{2\sqrt{5} }$

Cancel out √5 and divide 4 and 2

= 2//

∴$\frac{\sqrt{32} +\sqrt{48} }{\sqrt{8}+\sqrt{12} }$ = 2

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