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To rationalize a monomial denominator, multiply the numerator and denominator by a radical that will eliminate the radical in the denominator.
sqrt(210)/6
To simplify the given expression, we can first rewrite each radical as a quotient of two radicals.
sqrt(7/2)* sqrt(5/3)=sqrt(7)/sqrt(2)* sqrt(5)/sqrt(3)
Multiply fractions
sqrt(a)*sqrt(b)=sqrt(a* b)
Multiply
Finally, we can rationalize the denominator of the quotient. To rationalize a monomial denominator, we multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. Because the denominator is a square root, we need to multiply it by a square root that will give us a perfect square under the radical.
a/b=a * sqrt(6)/b * sqrt(6)
sqrt(a)*sqrt(b)=sqrt(a* b)
a^m*a^n=a^(m+n)
sqrt(a^2)=a
Multiply
We know that we have successfully rationalized the denominator because the radical has been eliminated.