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# How do you do square root of 98 divided by square root of 18?

Mar 3, 2018

$\frac{\sqrt{98}}{\sqrt{18}} = 2.333333333 \ldots$

#### Explanation:

For the equation:

$\frac{\sqrt{98}}{\sqrt{18}}$

You must

1. Find each square root

$\sqrt{98} = 9.899494937 \ldots$

$\sqrt{18} = 4.242640687 \ldots$

$\frac{9.899494937 \ldots}{4.242640687 \ldots} = 2.333333333 \ldots$

Or rounded up to
$2.3$ (repeating)

Mar 3, 2018

$\frac{7}{3}$

#### Explanation:

$\frac{\sqrt{98}}{\sqrt{18}}$

We can start by factoring out a perfect square from $\sqrt{98}$. Since $2 \cdot 49 = 98$, $\textcolor{b l u e}{\sqrt{2} \cdot \sqrt{49}} = \sqrt{98}$.

Next, let's factor out a perfect square from $\sqrt{18}$. Since $2 \cdot 9 = 18$, $\textcolor{b l u e}{\sqrt{2} \cdot \sqrt{9}} = \sqrt{18}$.

Our new fraction is as follows:

$\frac{\sqrt{2} \cdot \sqrt{49}}{\sqrt{2} \cdot \sqrt{9}}$

This can be simplified as:
$\frac{7 \cancel{\sqrt{2}}}{3 \cancel{\sqrt{2}}}$

$\frac{7}{3}$, as if you have the same things on the numerator and denominator, they will cancel.

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