# What is the square root of 84?

Mar 10, 2018

$\pm 2 \sqrt{21}$

#### Explanation:

We can break down $\sqrt{84}$ into the following:

$\sqrt{4} \cdot \sqrt{21}$

We are able to do this because of the property $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$

Where we can separate the radical into the product of the square root of its factors. $21$ and $4$ are factors of $84$.

In $\sqrt{4} \cdot \sqrt{21}$, we can simplify to get:

$\pm 2 \sqrt{21}$

*NOTE: The reason we have a$\pm$sign is because the square root of $4$ can be positive or negative $2$.

$\sqrt{21}$ has no perfect squares as factors, so this is the most we can simplify this expression.