# How do you simplify sqrt28/sqrt7?

Mar 18, 2018

$2$

#### Explanation:

Given: $\frac{\sqrt{28}}{\sqrt{7}}$

We got:

$\sqrt{28} = \sqrt{4 \cdot 7}$

$= \sqrt{4} \cdot \sqrt{7}$

$= 2 \cdot \sqrt{7}$

$2 \sqrt{7}$

So, the expression becomes:

$\frac{2 \sqrt{7}}{\sqrt{7}}$

$= \frac{2 \textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{7}}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{7}}}}}$

$= 2$

Mar 18, 2018

$\frac{\sqrt{28}}{\sqrt{7}} = \textcolor{b l u e}{2}$

#### Explanation:

Simplify:

$\frac{\sqrt{28}}{\sqrt{7}}$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{7}$.

$\frac{\sqrt{28} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Apply rule: $\sqrt{a} \sqrt{a} = a$

$\frac{\sqrt{28} \sqrt{7}}{7}$

Prime factorize $\sqrt{28}$.

$\frac{\sqrt{{2}^{2} \cdot 7} \sqrt{7}}{7}$

Apply rule: $\sqrt{{a}^{2}} = a$

$\frac{2 \sqrt{7} \sqrt{7}}{7}$

Apply rule: $\sqrt{a} \sqrt{a} = a$

$\frac{2 \times 7}{7}$

Cancel $7$.

$\frac{2 \times {\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}^{1}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} ^ 1$

Simplify.

$2$