# How do you write in simplified radical form of 4sqrt(48)?

Feb 5, 2015

You need to break down (find the prime factorization of) 48.

$4 \sqrt{6 \cdot 8}$
$4 \sqrt{2 \cdot 3 \cdot 4 \cdot 2}$
$4 \sqrt{2 \cdot 3 \cdot 2 \cdot 2 \cdot 2}$

Remember we are looking for pairs of two when we are looking for the square root.

We find that we have two sets of 2s. We will bring a 2 out for each set.

$4 \cdot 2 \cdot 2 \sqrt{3}$

Which gives me $16 \sqrt{3}$