How do you simplify sqrt(75)?

May 20, 2018

$\sqrt{75} = 5 \sqrt{3}$

Explanation:

$\sqrt{75} = \sqrt{{5}^{2} \cdot 3} = \sqrt{{5}^{2}} \cdot \sqrt{7} = 5 \cdot \sqrt{7}$

May 20, 2018

$5 \sqrt{3}$

Explanation:

We can simplify radicals using square numbers.

Start by listing the factors:

$75 \mathmr{and} 1$
$25 \mathmr{and} 3$
$15 \mathmr{and} 5$

$25$ is a squared number, so we can use $25$ and $3$

$\Rightarrow \sqrt{25} \times \sqrt{3}$

$\sqrt{25}$ can be simplified:

$\sqrt{25} = 5$

$\therefore$ $\Rightarrow 5 \sqrt{3}$