# How does the square root of 27 become 3 times the square root of 3?

Jul 23, 2015

Here's why that happens.

#### Explanation:

The number $27$ can actually be written as

$27 = 3 \cdot 3 \cdot 3$

Alternatively, you can write the same number as

27 = 3""^2 * 3

This means that when you take the square root of $27$ you can actually apply the product property of radicals, which tells you that

$\sqrt{A \cdot B} = \sqrt{A} \cdot \sqrt{B}$

$\sqrt{27} = \sqrt{3 {\text{^3 * 3) = sqrt(3}}^{2}} \cdot \sqrt{3} = \textcolor{g r e e n}{3 \cdot \sqrt{3}}$
This is why the square root of $27$ is equal to three times the square root of 3.