How do you simplify #\sqrt { 4a ^ { 3} b ^ { 5} }#?

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Answer 1 · 2018-01-22T02:37:56

#color(blue)(2asqrt(a)*b^2sqrt(b)#

Given the radical expression:

#color(red)(sqrt(4a^3b^5)#

#rArr sqrt(4)*sqrt(a^3)*sqrt(b^5)#

#rArr sqrt(2*2)*sqrt(a^2*a^1)*sqrt(b^4*b^1)#

#rArr 2*sqrt(a^2)*sqrt(a^1)*sqrt(b^4)*sqrt(b^1)#

#rArr 2*sqrt(a^2)*sqrt(a^1)*sqrt(b^2)*sqrt(b^2)*sqrt(b^1)#

#rArr 2*sqrt(a^2)*sqrt(a^1)*b*b*sqrt(b^1)#

#rArr 2*a*sqrt(a)*b^2*sqrt(b)#

Hence, we have our answer:

#color(blue)(2asqrt(a)*b^2sqrt(b)#

Answer 2 · 2018-01-22T03:40:51

#2 a b^2 sqrt(a b)#

Simplify

#sqrt(4 a^3 b^5#

To simplify, factor the expression into perfect squares as far as possible.

#sqrt(color(red)(2^2) (color(blue)(a^2) a) (color(orange)(b^4) b)#

Bring the square roots of the perfect squares outside, but leave the other factors inside

#color(red)2 color(blue)(a) color(orange)(b^2) sqrt(a b)#