Question

√32+√42 ÷ √8 +√12 simplify

Answer 1

Note: It should be 48 instead of 42 because √42 cannot be simplified.

Given:

Consider the given expression is

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

To find:

The simplified form of the given expression.

Solution:

We have,

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

It can be written as

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

$=\dfrac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}$

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

$=\dfrac{4}{2}$

$=2$

Therefore, the simplified form of the given expression is 2.