# How do you simplify 3sqrt50*sqrt22?

May 5, 2018

$30 \sqrt{11}$

#### Explanation:

$3 \sqrt{50} \cdot \sqrt{22}$

$3 \sqrt{25 \cdot 2} \cdot \sqrt{22} \rightarrow 25$ is a perfect square and can be taken out of the radical

$3 \cdot 5 \sqrt{2} \cdot \sqrt{22}$

$15 \sqrt{2} \cdot \sqrt{22}$

$15 \sqrt{2 \cdot 22}$

$15 \sqrt{44}$

$15 \sqrt{4 \cdot 11} \rightarrow 4$ is a perfect square

$15 \cdot 2 \sqrt{11}$

$30 \sqrt{11}$

I'm going to try to write out your question mathematically:
$\sqrt{50 \times \sqrt{22}}$

#### Explanation:

To solve this exceedingly complicated question, let's start by converting everything into indices.

But first, we should simplify your equation:
$\sqrt{\sqrt{55000}}$
Now the question will be written in indicial form as:
${\left({55000}^{\frac{1}{2}}\right)}^{\frac{1}{3}}$

By the power law of indices $\to$ ${\left({a}^{m}\right)}^{n} = {a}^{m n}$, this would make the indices $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.
Therefore, the question will now become:
${55000}^{\frac{1}{6}}$
$= \sqrt{55000}$
$= 50 \sqrt{22}$
In surd form.

I hope this helps!

May 5, 2018

$30 \sqrt{11}$

#### Explanation:

$3 \sqrt{50} \cdot \sqrt{22}$

$\therefore = 3 \sqrt{2 \cdot 5 \cdot 5} \cdot \sqrt{2 \cdot 11}$

$\therefore = \sqrt{5} \cdot \sqrt{5} = 5$

$\therefore = 3 \cdot 5 \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{11}$

$\therefore = 15 \sqrt{2} \cdot \sqrt{2} \cdot \sqrt{11}$

$\therefore = \sqrt{2} \cdot \sqrt{2} = 2$

$\therefore = 2 \cdot 15 \cdot \sqrt{11}$

$\therefore = 30 \sqrt{11}$