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.
