# How do you simplify sqrt(128)?

Mar 14, 2016

$\sqrt{128} = 8 \sqrt{2}$

#### Explanation:

$\sqrt{128} = \sqrt{64 \cdot 2} = \sqrt{64} \sqrt{2} = 8 \sqrt{2}$

Mar 14, 2016

$\sqrt{128} = 8 \cdot \sqrt{2}$

#### Explanation:

The process here is to simplify radicals. Using a tree diagram, you can break down 128 into it's constituent prime number factors.

$$                                           128
/    \
2     64
/   \
2   32
/   \
2   16
/   \
2    8
/   \
2   4
/   \
2   2


Counting the prime factors, the number 2 shows up seven times, so

$128 = {2}^{7}$, which gives us $\sqrt{128} = \sqrt{{2}^{7}} = \sqrt{{2}^{6} \cdot 2} = {2}^{3} \cdot \sqrt{2} = 8 \cdot \sqrt{2}$