McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
3. Simplifying Radical Expressions
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Exercise 10 Page 248

To rationalize a monomial denominator, multiply the numerator and denominator by a radical that will eliminate the radical in the denominator.

D

Practice makes perfect
To simplify the given expression, we can first rewrite the radical as a quotient of two radicals. sqrt(45/10)=sqrt(45)/sqrt(10) Now, 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.
sqrt(45)/sqrt(10)
sqrt(45)* sqrt(10)/sqrt(10)* sqrt(10)
sqrt(45* 10)/sqrt(10* 10)
sqrt(3* 3* 5* 5* 2)/sqrt(10* 10)
sqrt(3^2* 5^2* 2)/sqrt(10^2)
sqrt(3^2)sqrt(5^2)sqrt(2)/sqrt(10^2)
3(5)sqrt(2)/10
3sqrt(2)/2
We know that we have successfully rationalized the denominator because the radical has been eliminated. Therefore, the correct choice is D.