Exercise 41 Page 249

To simplify the given expression, we can first rewrite each radical as a quotient of two radicals. sqrt(3/16)* sqrt(9/5)=sqrt(3)/sqrt(16)* sqrt(9)/sqrt(5)Now, we can evaluate the numerical value of radical expressions and multiply the fractions.

sqrt(3)/sqrt(16)* sqrt(9)/sqrt(5)

CalcRoot

Calculate root

sqrt(3)/4* 3/sqrt(5)

MultFrac

Multiply fractions

3sqrt(3)/4sqrt(5)

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.

3sqrt(3)/4sqrt(5)

ExpandFrac

a/b=a * sqrt(5)/b * sqrt(5)

3sqrt(3)* sqrt(5)/4sqrt(5)* sqrt(5)

ProdSqrt

sqrt(a)*sqrt(b)=sqrt(a* b)

3sqrt(3* 5)/4sqrt(5* 5)

MultPow

a^m*a^n=a^(m+n)

3sqrt(3* 5)/4sqrt(5^2)

SqrtPowToNumber

sqrt(a^2)=a

3sqrt(3* 5)/4(5)

Multiply

Multiply

3sqrt(15)/20

We know that we have successfully rationalized the denominator because the radical has been eliminated.