What is the simplified form of 3sqrt(5c) times sqrt(15^3)35c×153?

1 Answer
Sep 7, 2017

225sqrt3sqrtc2253c

Explanation:

3\sqrt{5c}\sqrt{15^3}35c153

=3\sqrt{5}\sqrt{15^3}\sqrt{c}=35153c Reason: (\sqrt{5c}=\sqrt{5}\sqrt{c}5c=5c)

=3\cdot \15\sqrt{5}\sqrt{15}\sqrt{c}=315515c Reason: (\sqrt{15^3}=15\sqrt{15}153=1515)

=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{15}=35c5315 Reason:(15=3\cdot \515=35)

=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{5\cdot \3}=35c5353 Reason:(15=3\cdot \515=35)

=3\sqrt{5}\sqrt{c}\cdot \5\cdot \3\sqrt{5}\sqrt{3}=35c5353 Reason:(\sqrt[n]^{ab}=\sqrt[n]^{a}\sqrt[n]^{b}nab=nanb)

=5\cdot \3^{\frac{5}{2}}\sqrt{5}\sqrt{5}\sqrt{c}=535255c Reason:(a^b\cdot \a^c=a^{b+c}abac=ab+c)

=3^2\cdot \5^2\sqrt{3}\sqrt{c}=32523c Reason:(\:a^b\cdot \:a^c=a^{b+c}:ab:ac=ab+c)

=225\sqrt{3}\sqrt{c}=2253c Refined answer