# What is the square root of 464?

$4 \sqrt{29}$
$\sqrt{464} = \sqrt{2 \cdot 232} = \sqrt{2 \cdot 2 \cdot 116} = \sqrt{2 \cdot 2 \cdot 2 \cdot 58} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 29} = \sqrt{16 \cdot 29}$
At this point, we can't divide $29$ anymore, because it is a prime number. You can split this expression in:
$\sqrt{16} \cdot \sqrt{29} = 4 \sqrt{29}$