McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Simplifying Radical Expressions
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Exercise 42 Page 249

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

sqrt(210)/6

Practice makes perfect
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)Now, we can multiply the fractions.
sqrt(7)/sqrt(2)* sqrt(5)/sqrt(3)
sqrt(7)sqrt(5)/sqrt(2) sqrt(3)
sqrt(7* 5)/sqrt(2* 3)
sqrt(35)/sqrt(6)
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.
sqrt(35)/sqrt(6)
sqrt(35)* sqrt(6)/sqrt(6)* sqrt(6)
sqrt(35* 6)/sqrt(6* 6)
sqrt(35* 6)/sqrt(6^2)
sqrt(35* 6)/6
sqrt(210)/6
We know that we have successfully rationalized the denominator because the radical has been eliminated.