How do you simplify 33/sqrt99?

2 Answers
Jim G.
Mar 19, 2017

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

mason m
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

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