# What is the square root of 464?

Oct 16, 2015

#### Answer:

$4 \sqrt{29}$

#### Explanation:

This square root isn't the square root of a perfect square. The only thing we can do is to simplify the expression. First let's try dividing by two until we can't anymore:
$\sqrt{464} = \sqrt{2 \cdot 232} = \sqrt{2 \cdot 2 \cdot 116} = \sqrt{2 \cdot 2 \cdot 2 \cdot 58} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 29} = \sqrt{16 \cdot 29}$

At this point, we can't divide $29$ anymore, because it is a prime number. You can split this expression in:
$\sqrt{16} \cdot \sqrt{29} = 4 \sqrt{29}$