How do you simplify sqrt(14)/sqrt(21)√14√21?

1 Answer
MeneerNask
Oct 1, 2015

Note that 14=2*7and 21=3*714=2⋅7and21=3⋅7

Explanation:

We can now rewrite:

sqrt14=sqrt(2*7)=sqrt2*sqrt7√14=√2⋅7=√2⋅√7, and:
sqrt21=sqrt(3*7)=sqrt3*sqrt7√21=√3⋅7=√3⋅√7

Putting this together, we get:

=(sqrt2*cancelsqrt7)/(sqrt3*cancelsqrt7)=sqrt2/sqrt3

If you multiply both halves of the fraction by sqrt3:

=(sqrt3*sqrt2)/(sqrt3*sqrt3)=sqrt6/3=1/3 sqrt6

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