How do you simplify #33/sqrt99#?

2 Answers
Mar 19, 2017

Answer:

#sqrt11#

Explanation:

#sqrt99=sqrt(9xx11)=sqrt9xxsqrt11=3sqrt11#

#rArr(33)/(sqrt99)=cancel(33)^(11)/(cancel(3)^1sqrt11)=11/sqrt11#

#color(blue)" Rationalising the denominator"#

#rArr11/sqrt11xxsqrt11/sqrt11#

#=(cancel(11)^1sqrt11)/cancel(11)^1#

#=sqrt11#

Mar 19, 2017

We can also do this in one fell swoop using prime factorization:

#33/sqrt(99)=(3xx11)/(3^2xx11)^(1/2)=(3xx11)/(3xx11^(1/2))=11^(1-1/2)=11^(1/2)=sqrt11#