McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Study Guide and Review
Continue to next subchapter

Exercise 26 Page 265

Begin by multiplying the expressions inside the radicals. To rationalize a monomial denominator, we multiply the numerator and denominator by a radical that will eliminate the radical in the denominator.

sqrt(30)/10

Practice makes perfect
We can simplify this expression by multiplying the expressions inside the radicals.
sqrt(2/5)*sqrt(3/4)
sqrt(2/5* 3/4)
sqrt(2*3/5* 4)
sqrt(6/20)
Now, let's rewrite the radical as a quotient of two radicals. sqrt(6/20)=sqrt(6)/sqrt(20) 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(6)/sqrt(20)
sqrt(6)* sqrt(20)/sqrt(20)* sqrt(20)
sqrt(6)* sqrt(20)/20
sqrt(6*20)/20
We know that we have successfully rationalized the denominator because the radical has been eliminated. However, our fraction can still simplified a bit further. Let's try!
sqrt(6*20)/20
â–Ľ
Simplify
sqrt(2*3*2*10)/20
sqrt(2*2*3*10)/20
sqrt(2^2 *3*10)/20
sqrt(2^2)*sqrt(3*10)/20
2*sqrt(3*10)/20
2sqrt(30)/20
sqrt(30)/10