How do you evaluate #\sqrt { 3^ { 2} \cdot 2^ { 2} \cdot 5^ { 4} }#?

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Answer 1 · 2017-06-14T03:26:23

See a solution process below:

Using this rule for radical multiplication we can rewrite this expression as:

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

#sqrt(color(red)(3^2) * color(blue)(2^2) * color(green)(5^4)) => #

#sqrt(color(red)(3^2)) * sqrt(color(blue)(2^2)) * sqrt(color(green)(5^4)) =>#

#3 * 2 * 5^2 =>#

#6 * 25 =>#

#150#

Answer 2 · 2017-06-14T03:33:10

#150#

Expression #= sqrt(3^2*2^2*5^4)#

#= sqrt((3*3)*(2*2)*(5*5)*(5*5))#

Since #sqrt((a*a)) =a#

Any pair of numbers may be removed from the #sqrt# one time.

#:.# Expression #= 3*2*5*5#

#=150#