# How does the square root of 12 become 2 times the square root of 3?

Jul 6, 2015

$\sqrt{12} = 2 \sqrt{3}$

#### Explanation:

Let's factor the term inside the radical.

sqrt12 = sqrt(2×2×3) = sqrt(2^2×3)

We know that

sqrt(xy) = sqrtx × sqrt y

So

sqrt12 = sqrt(2^2×3) = sqrt(2^2) × sqrt3

sqrt12 = 2 × sqrt3

$\sqrt{12} = 2 \sqrt{3}$