How do you simplify #\sqrt { \frac { 9a ^ { 3} } { 4z ^ { 4} } } #?

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Answer 1 · 2017-11-30T19:00:44

See a solution process below:

First, use this rule for radicals to rewrite the expression:

#sqrt(color(red)(a)/color(blue)(b)) = sqrt(color(red)(a))/sqrt(color(blue)(b))#

#sqrt(color(red)(9a^3)/color(blue)(4z^4)) => sqrt(color(red)(9a^3))/sqrt(color(blue)(4z^4)) => sqrt(9a^2 * a)/(2z^2)#

We can now use this rule of radicals to rewrite the numerator and complete the simplification:

#(sqrt(color(red)(9a^2) * color(blue)(a)))/(2z^2) => (sqrt(color(red)(9a^2)) * sqrt(color(blue)(a)))/(2z^2) => (3asqrt(a))/(2z^2)#

Answer 2 · 2017-11-30T19:22:40

See the solution and answer below...

#\sqrt { \frac { 9a ^ { 3} } { 4z ^ { 4} } } #

To simplify, remove the #sqrt#

Remember #sqrta = a^(1/2)#

#((9a^3)/(4z^4))^(1/2)#

#(((3^2)(a^3))/((2^2)(z^4)))^(1/2)#

#((3^(2 xx 1/2))(a^(3 xx 1/2)))/((2^(2 xx 1/2))(z^(4 xx 1/2))#

#((3^1) (a^(3 /2)))/((2^1)(z^(2))#

#(3a^(3 /2))/(2z^(2))#