What is the square root of 84?

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Answer 1 · 2018-03-10T18:06:53

$\pm 2 \sqrt{21}$ $+-2sqrt21$

We can break down $\sqrt{84}$ $sqrt84$ into the following:

$\sqrt{4} \cdot \sqrt{21}$ $sqrt4*sqrt21$

We are able to do this because of the property $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ $sqrt(ab)=sqrta*sqrtb$

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

In $\sqrt{4} \cdot \sqrt{21}$ $sqrt4*sqrt21$ , we can simplify to get:

$\pm 2 \sqrt{21}$ $+-2sqrt21$

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

$\sqrt{21}$ $sqrt21$ has no perfect squares as factors, so this is the most we can simplify this expression.