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

1 Answer
Sep 7, 2017

Answer:

#225sqrt3sqrtc#

Explanation:

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

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

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

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

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

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

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

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

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