How do you simplify $3 \sqrt{5 c} \times {\sqrt{15}}^{3}$ $3sqrt(5c) times sqrt15^3$ ?

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How do you simplify $3 \sqrt{5 c} \times {\sqrt{15}}^{3}$ $3sqrt(5c) times sqrt15^3$ ?

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Answer 1 · 2018-02-22T03:04:16

$225 \sqrt{3 c}$ $225sqrt(3c)$

Explanation:

$3 \sqrt{5 c} {\sqrt{15}}^{3}$ $3sqrt(5c)sqrt(15)^3$

First, we can simplify ${\sqrt{15}}^{3}$ $sqrt(15)^3$ .
${\sqrt{15}}^{3} = \sqrt{15} \cdot \sqrt{15} \cdot \sqrt{15} = 15 \cdot \sqrt{15}$ $sqrt(15)^3 = sqrt15*sqrt15*sqrt15 = 15*sqrt15$
$3 \cdot 15 \sqrt{5 c} \sqrt{15}$ $3*15sqrt(5c)sqrt15$
$45 \sqrt{5 c} \sqrt{15}$ $45sqrt(5c)sqrt15$

Then, we can consolidate and simplify our two irrationals.
$\sqrt{α} \cdot \sqrt{β} = \sqrt{α β}$ $sqrt(alpha)*sqrt(beta) = sqrt(alphabeta)$
$\sqrt{5 c} \sqrt{15} = \sqrt{75 c}$ $sqrt(5c)sqrt15 = sqrt(75c)$
$45 \sqrt{75 c}$ $45sqrt(75c)$
$\sqrt{75 c} = \sqrt{25} \sqrt{3 c}$ $sqrt(75c) = sqrt25sqrt(3c)$
$45 \cdot 5 \sqrt{3 c}$ $45*5sqrt(3c)$

This brings us to a simplification of the original statement:
$225 \sqrt{3 c}$ $225sqrt(3c)$

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How do you simplify $3 \sqrt{5 c} \times {\sqrt{15}}^{3}$ $3sqrt(5c) times sqrt15^3$ ?

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How do you simplify $3 \sqrt{5 c} \times {\sqrt{15}}^{3}$ $3sqrt(5c) times sqrt15^3$ ?