# How do you find the simplified radical form of 54?

Jun 5, 2018

$3 \sqrt{6}$

#### Explanation:

To simplify $\sqrt{54}$

Begin by finding the prime factors of $54$

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For each factor pair place one factor outside of the radical and each unpaired factor place inside the radical.

$3 \sqrt{6}$

#### Explanation:

An alternate way of doing the simplification:

We can take $\sqrt{54}$ and break down 54 inside the radical:

$\sqrt{3 \times 3 \times 3 \times 2}$

Remember that the square root and square operations are opposite - they cancel each other out. And so if we can find squares, we can cancel them against the square root:

$\sqrt{{3}^{2} \times 3 \times 2}$

And if we want, we can put the square into its own radical:

$\sqrt{{3}^{2}} \sqrt{3 \times 2}$

Cancel the square against the square root, and then simplify the other root:

$3 \sqrt{6}$