How do you simplify (4 sqrt 45) / (5 sqrt 8)?

2 Answers
May 3, 2018

$\frac{3 \sqrt{10}}{5}$

Explanation:

Remember that perfect squares can be taken out of radicals

$\frac{4 \sqrt{45}}{5 \sqrt{8}}$

$\frac{4 \sqrt{9 \cdot 5}}{5 \sqrt{4 \cdot 2}}$

(4*3sqrt5)/(5*2sqrt2

$\frac{12 \sqrt{5}}{10 \sqrt{2}}$

$\frac{6 \sqrt{5}}{5 \sqrt{2}} \rightarrow$ Don't forget to rationalize the denominator

$\frac{6 \sqrt{5 \cdot 2}}{5 \sqrt{2 \cdot 2}}$

$\frac{6 \sqrt{10}}{5 \sqrt{4}}$

$\frac{6 \sqrt{10}}{10}$

$\frac{3 \sqrt{10}}{5}$

May 3, 2018

$14 \frac{2}{5}$ or $14.4$

Explanation:

$\frac{4 \sqrt{45}}{5 \sqrt{8}}$

First, find the largest factors of $45$ and $8$ that can be square rooted.
$9 \cdot 5 = 45$, and $\sqrt{9} = 3$
$4 \cdot 2 = 8$, and $\sqrt{4} = 2$

Now we put it back into the expression like this:
(4sqrt(9 * 5))/(5sqrt(4 * 2)

Split up the square root:
$\frac{4 \sqrt{9} \sqrt{5}}{5 \sqrt{4} \sqrt{2}}$

Take square root of $9$ and $4$:
$\frac{4 \cdot 3 \sqrt{5}}{5 \cdot 2 \sqrt{2}}$

Multiply:
$\frac{12 \sqrt{5}}{5 \sqrt{2}}$

Square numerator and denominator:
${\left(12 \sqrt{5}\right)}^{2} / {\left(5 \sqrt{2}\right)}^{2}$

$\frac{144 \cdot 5}{25 \cdot 2}$

$\frac{720}{50}$

Divide:
$14 \frac{2}{5}$ or $14.4$

Hope this helps!