# How do you simplify sqrt75/sqrt3?

Jul 29, 2018

$\pm 5$

#### Explanation:

$\text{using the "color(blue)"law of radicals}$

•color(white)(x)sqrta/sqrtbhArrsqrt(a/b)

$\frac{\sqrt{75}}{\sqrt{3}} = \sqrt{\frac{75}{3}} = \sqrt{25} = \pm 5$

Jul 29, 2018

$\pm 5$

#### Explanation:

We can rewrite $\sqrt{75}$ as $\sqrt{25} \sqrt{3}$. We now have:

$\frac{\sqrt{25} \sqrt{3}}{\sqrt{3}}$

We can cancel out common factors in the numerator and denominator to get

$\frac{\sqrt{25} \cancel{\sqrt{3}}}{\cancel{\sqrt{3}}} = \sqrt{25} = \pm 5$

Another way to approach this is leveraging the radical law

$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. With this in mind, we can rewrite this entire expression as

$\sqrt{\frac{75}{3}} = \sqrt{25} = \pm 5$

Hope this helps!