# How do you simplify sqrt50/(3sqrt2)?

Apr 15, 2018

$\frac{5}{3}$

#### Explanation:

$\frac{\sqrt{50}}{3 \sqrt{2}} =$

$\frac{\sqrt{25 \cdot 2}}{3 \sqrt{2}} =$

$\frac{5 \cancel{\sqrt{2}}}{3 \cancel{\sqrt{2}}} =$

$\frac{5}{3}$

Apr 15, 2018

$\frac{5}{3}$

#### Explanation:

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

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

$\Rightarrow \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}$

$\Rightarrow \frac{\sqrt{50}}{3 \sqrt{2}} = \frac{5 \cancel{\sqrt{2}}}{3 \cancel{\sqrt{2}}} = \frac{5}{3}$

Apr 15, 2018

$\pm \frac{5}{3}$

#### Explanation:

Let's start by thinking about the number $50$, not $\sqrt{50}$. We know its factors are:

• $25$ and $2$
• $10$ and $5$

So the factors of $\sqrt{50}$ are:

• $\textcolor{b l u e}{\sqrt{25}}$ and $\textcolor{b l u e}{\sqrt{2}}$
• $\sqrt{10}$ and $\sqrt{5}$

We can use the first set of factors to rewrite our expression as

$\frac{\textcolor{b l u e}{\sqrt{25} \cdot \cancel{\sqrt{2}}}}{3 \cancel{\sqrt{2}}}$

The $\sqrt{2}$ will cancel on the top and bottom, and we're left with

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

Which can be simplified to

$\pm \frac{5}{3}$

Hope this helps!