How do you rationalize the denominator and simplify #sqrt21/sqrt6#?

1 Answer
Mar 15, 2016

Answer:

#sqrt(106)/6#

Explanation:

#1#. Since the denominator of the fraction contains a radical, start by multiplying the numerator and denominator by #sqrt(6)/sqrt(6)#. Note that #sqrt(6)/sqrt(6)=1#, so that value of the fraction remains the same.

#sqrt(21)/sqrt(6)#

#=sqrt(21)/sqrt(6)(sqrt(6)/sqrt(6))#

#2#. Simplify.

#=sqrt(21*6)/6#

#=color(green)(|bar(ul(color(white)(a/a)sqrt(106)/6color(white)(a/a)|)))#