How do you simplify #sqrt45/(4sqrt81)#?

1 Answer
Mar 15, 2016

Answer:

#sqrt(5)/12#

Explanation:

#1#. Start by multiplying the numerator and denominator by #sqrt(81)/sqrt(81)# to get rid of the radical in the denominator. Note that the value of the fraction would not change since #sqrt(81)/sqrt(81)=1#.

#sqrt(45)/(4sqrt(81))#

#=sqrt(45)/(4sqrt(81))(sqrt(81)/sqrt(81))#

#2#. Simplify.

#=sqrt(45*81)/(4(sqrt(81)sqrt(81)))#

#=sqrt(3645)/(4(81))#

#=sqrt(3645)/324#

#3#. Using a perfect square, break down the radical in the numerator.

#=sqrt(27^2*5)/324#

#4#. Simplify.

#=(27sqrt(5))/324#

#=(color(red)cancelcolor(black)27^1sqrt(5))/color(red)cancelcolor(black)324^12#

#=color(green)(|bar(ul(color(white)(a/a)sqrt(5)/12color(white)(a/a)|)))#