How do you simplify $\sqrt{100 y^{2} z^{4}}$ $sqrt(100y^2z^4)$ ?

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Answer 1 · 2015-11-07T15:30:19

$= 10 y z^{2}$ $=color(blue)(10yz^2$

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

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

$100 = 2 \cdot 2 \cdot 5 \cdot 5 = 2^{2} \cdot 5^{2}$ $100=2*2*5*5=color(purple)(2^2*5^2$

So,
$\sqrt{100 y^{2} z^{4}} = \sqrt{2^{2} \cdot 5^{2} \cdot y^{2} \cdot z^{4}}$ $sqrt(100y^2z^4)=sqrt(color(purple)(2^2*5^2) *y^2*z^4)$

$= \sqrt{2^{2} \cdot 5^{2} \cdot y \cdot y \cdot z^{2} \cdot z^{2}}$ $=sqrt(color(purple)(2^2*5^2) *color(blue)(y *y) *color(green)(z^2*z^2)$

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

$= 10 y z^{2}$ $=color(blue)(10yz^2$

How do you simplify sqrt(100y^2z^4)√100y2z4sqrt(100y^2z^4)?