√32+√42 ÷ √8 +√12 simplify

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

Given:

Consider the given expression is

[tex]\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}[/tex]

It can be written as

[tex]=\dfrac{\sqrt{16\times 2}+\sqrt{16\times 3}}{\sqrt{4\times 2}+\sqrt{4\times 3}}[/tex]

[tex]=\dfrac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}[/tex]

[tex]=\dfrac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}[/tex]

[tex]=\dfrac{4}{2}[/tex]

[tex]=2[/tex]

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

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