What is the simplified form of $3 \sqrt{5 c} \times \sqrt{15^{3}}$ $3sqrt(5c) times sqrt(15^3)$ ?

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What is the simplified form of $3 \sqrt{5 c} \times \sqrt{15^{3}}$ $3sqrt(5c) times sqrt(15^3)$ ?

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Answer 1 · 2017-09-07T12:54:57

$225 \sqrt{3} \sqrt{c}$ $225sqrt3sqrtc$

Explanation:

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

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

$= 3 \cdot 15 \sqrt{5} \sqrt{15} \sqrt{c}$ $=3\cdot \15\sqrt{5}\sqrt{15}\sqrt{c}$ Reason: ( $\sqrt{15^{3}} = 15 \sqrt{15}$ $\sqrt{15^3}=15\sqrt{15}$ )

$= 3 \sqrt{5} \sqrt{c} \cdot 5 \cdot 3 \sqrt{15}$ $=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{15}$ Reason:( $15 = 3 \cdot 5$ $15=3\cdot \5$ )

$= 3 \sqrt{5} \sqrt{c} \cdot 5 \cdot 3 \sqrt{5 \cdot 3}$ $=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{5\cdot \3}$ Reason:( $15 = 3 \cdot 5$ $15=3\cdot \5$ )

$= 3 \sqrt{5} \sqrt{c} \cdot 5 \cdot 3 \sqrt{5} \sqrt{3}$ $=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{5}\sqrt{3}$ Reason:( ${\sqrt{n}}^{a b} = {\sqrt{n}}^{a} {\sqrt{n}}^{b}$ $\sqrt[n]^{ab}=\sqrt[n]^{a}\sqrt[n]^{b}$ )

$= 5 \cdot 3^{\frac{5}{2}} \sqrt{5} \sqrt{5} \sqrt{c}$ $=5\cdot \3^{\frac{5}{2}}\sqrt{5}\sqrt{5}\sqrt{c}$ Reason:( $a^{b} \cdot a^{c} = a^{b + c}$ $a^b\cdot \a^c=a^{b+c}$ )

$= 3^{2} \cdot 5^{2} \sqrt{3} \sqrt{c}$ $=3^2\cdot \5^2\sqrt{3}\sqrt{c}$ Reason:( $: a^{b} \cdot : a^{c} = a^{b + c}$ $\:a^b\cdot \:a^c=a^{b+c}$ )

$= 225 \sqrt{3} \sqrt{c}$ $=225\sqrt{3}\sqrt{c}$ Refined answer

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What is the simplified form of $3 \sqrt{5 c} \times \sqrt{15^{3}}$ $3sqrt(5c) times sqrt(15^3)$ ?

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What is the simplified form of 3√5c×√1533sqrt(5c) times sqrt(15^3)?

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What is the simplified form of $3 \sqrt{5 c} \times \sqrt{15^{3}}$ $3sqrt(5c) times sqrt(15^3)$ ?