How do you rationalize the denominator and simplify #sqrt (33/77)#?

1 Answer
Mar 15, 2016

Answer:

#sqrt(21)/7#

Explanation:

#1#. Since the denominator of the fraction contains a radical, start by multiplying the numerator and denominator by #sqrt(77)/sqrt(77)#. Note that #sqrt(77)/sqrt(77)=1#, so that value of the fraction remains the same.

#sqrt(33)/sqrt(77)#

#=sqrt(33)/sqrt(77)(sqrt(77)/sqrt(77))#

#2#. Simplify.

#=sqrt(33*77)/77#

#=sqrt(2541)/77#

#3#. Use a perfect square to break down the radical in the numerator.

#=sqrt(11^2*21)/77#

#4#. Simplify.

#=(11sqrt(21))/77#

#=(color(red)cancelcolor(black)11^1sqrt(21))/color(red)cancelcolor(black)77^7#

#=color(green)(|bar(ul(color(white)(a/a)sqrt(21)/7color(white)(a/a)|)))#