# How do you simplify sqrt200-sqrt32?

May 7, 2016

$6 \sqrt{2}$

#### Explanation:

$\sqrt{2 \times {10}^{2}} - \sqrt{2 \times {4}^{2}}$

$10 \sqrt{2} - 4 \sqrt{2}$
'~~~~~~~~~~~~~~~~~~~~~~
compare to $10 x - 4 x = 6 x$
'~~~~~~~~~~~~~~~~~~~~~~~~~~
$\implies 6 \sqrt{2}$

May 7, 2016

$6 \sqrt{2}$

#### Explanation:

Breaking the values down into the prime factors is always possible, but sometimes a bit tedious and often unnecessary if square numbers are recognised as being factors. 200 = 100 x 2 is an obvious example.

$\sqrt{200} - \sqrt{32}$
= sqrt(100xx2) - sqrt(16xx2
= $10 \sqrt{2} - 4 \sqrt{2}$
= $\sqrt{2} \left(10 - 4\right)$
= $6 \sqrt{2}$