# How do you simplify sqrt(350)?

Jan 7, 2016

$5 \sqrt{14}$

#### Explanation:

search for the factors of $350$ looking for one that is a perfect square.

In this case $25 \times 14$

$25$ being the perfect square.

$\sqrt{350} = \sqrt{25 \times 14}$

now $\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ (so long as at least one of $a$ and $b$ is not negative)

$\Rightarrow \sqrt{25 \times 14} = \sqrt{25} \times \sqrt{14}$

The factors of $14$ do not contain any square numbers apart from $1$ and so $\sqrt{14}$ cannot be simplified any further.

$\Rightarrow \sqrt{350} = 5 \sqrt{14}$

Jan 7, 2016

$5 \times \sqrt{14}$
$350 = 35 \times 10 = 7 \times 5 \times 2 \times 5 = 2 \times {5}^{2} \times 7$
$\sqrt{350} = \sqrt{2 \times {5}^{2} \times 7} = \sqrt{{5}^{2}} \times \sqrt{2 \times 7} =$
$5 \times \sqrt{2 \times 7} = 5 \times \sqrt{14}$