How do you simplify $\sqrt{\frac{2 g^{3}}{5 z}}$ $sqrt((2g^3)/(5z))$ ?

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How do you simplify $\sqrt{\frac{2 g^{3}}{5 z}}$ $sqrt((2g^3)/(5z))$ ?

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Answer 1 · 2015-09-22T05:19:35

$\frac{\sqrt{10 g z} \cdot g}{5 z}$ $(sqrt(10gz)*g)/(5z)$

Explanation:

First, begin by "distributing" the square root sign to the numerator and denominator:
$\frac{\sqrt{2 g^{3}}}{\sqrt{5 z}}$ $sqrt(2g^3)/(sqrt(5z)$
Now simplify the top:
$\frac{\sqrt{2} \sqrt{g^{3}}}{\sqrt{5 z}}$ $(sqrt(2)sqrt(g^3))/sqrt(5z)$ (because $\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$ )

$\frac{\sqrt{2} \cdot g \sqrt{g}}{\sqrt{5 z}}$ $(sqrt(2)*gsqrt(g))/sqrt(5z)$ (for example, $\sqrt{2^{3}} = \sqrt{8} = 2 \sqrt{2}$ $sqrt(2^3) = sqrt(8) = 2sqrt(2)$ )

Since it isn't proper to have a square root in the denominator, we take it out by multiplying by $\frac{\sqrt{5 z}}{\sqrt{5 z}}$ $sqrt(5z)/sqrt(5z)$ .

$\frac{\sqrt{2} \cdot g \sqrt{g}}{\sqrt{5 z}} \cdot \frac{\sqrt{5 z}}{\sqrt{5 z}}$ $(sqrt(2)*gsqrt(g))/sqrt(5z)*sqrt(5z)/sqrt(5z)$

$\frac{\sqrt{2} \cdot g \sqrt{g} \cdot \sqrt{5 z}}{5 z}$ $(sqrt(2)*gsqrt(g)*sqrt(5z))/(5z)$ ( $\sqrt{5 z} \cdot \sqrt{5 z} = 5 z$ $sqrt(5z)*sqrt(5z) = 5z$ )

We can now finally collect all of our radicals (square roots) into one neat sign:

$\frac{\sqrt{10 z g} \cdot g}{5 z}$ $(sqrt(10zg)*g)/(5z)$ (remember that $\sqrt{a} \sqrt{b} \sqrt{c} = \sqrt{a b c}$ $sqrt(a)sqrt(b)sqrt(c) = sqrt(abc)$ )

And that is the final answer.

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How do you simplify $\sqrt{\frac{2 g^{3}}{5 z}}$ $sqrt((2g^3)/(5z))$ ?

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