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Simplify the following: 1. $ \sqrt{18} + \sqrt{32}$ 2. $\sqrt{20} + \sqrt{45}$
Given :
The given expressions are,
1. $ \sqrt{18} + \sqrt{32}$.
2. $\sqrt{20} + \sqrt{45}$.
To do :
We have to simplify the given expressions.
Solution :
We know that,
$b\sqrt{a} + c\sqrt{a} = (b+c)\sqrt{a}$
1. $ \sqrt{18} + \sqrt{32}$
$ \sqrt{18} + \sqrt{32} = \sqrt{3 \times 3 \times 2} + \sqrt{4 \times 4 \times 2}$
$= 3\sqrt{2} + 4\sqrt{2}$
$ = (3+4)\sqrt{2}$
$= 7\sqrt{2}$
Therefore, the value of $ \sqrt{18} + \sqrt{32}$ is $7\sqrt{2}$.
2. $ \sqrt{20} + \sqrt{45}$
$ \sqrt{20} + \sqrt{45} = \sqrt{2 \times 2 \times 5} + \sqrt{3 \times 3 \times 5}$
$= 2\sqrt{5} + 3\sqrt{5}$
$ = (2+3)\sqrt{5}$
$= 5\sqrt{5}$
Therefore, the value of $ \sqrt{20} + \sqrt{45}$ is $5\sqrt{5}$.