# How do you simplify sqrt(100y^2z^4)?

Nov 7, 2015

=color(blue)(10yz^2

#### Explanation:

$\sqrt{100 {y}^{2} {z}^{4}}$

First we simplify $100$ by prime factorisation(express a number as a product of its prime factors):

100=2*2*5*5=color(purple)(2^2*5^2

So,
$\sqrt{100 {y}^{2} {z}^{4}} = \sqrt{\textcolor{p u r p \le}{{2}^{2} \cdot {5}^{2}} \cdot {y}^{2} \cdot {z}^{4}}$

=sqrt(color(purple)(2^2*5^2) *color(blue)(y *y) *color(green)(z^2*z^2)

$= 2 \cdot 5 \cdot y \cdot {z}^{2}$

=color(blue)(10yz^2