McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
1. Points, Lines, and Planes
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Exercise 69 Page 12

To rationalize the denominator, multiply the numerator and denominator by a radical that will get rid of the radical in the denominator.

sqrt(2)/2

Practice makes perfect

To rationalize a radical expression in the denominator of a fraction, we have to multiply it by a fraction equivalent to 1 such that the resulting denominator is a rational number. Remember that we have to multiply both the numerator and the denominator. Consider the following for any rational numbers a and b. a/sqrt(b)=a/sqrt(b)*sqrt(b)/sqrt(b)=a sqrt(b)/bIn this case, we have to multiply the given expression by sqrt(18)sqrt(18).

3/sqrt(18)* sqrt(18)/sqrt(18)
3*sqrt(18)/sqrt(18)*sqrt(18)
3*sqrt(18)/18

Note, that we can simplify this expression further.

3*sqrt(18)/18
â–¼
Simplify root
3*sqrt(9* 2)/18
3*sqrt(9)*sqrt(2)/18
3* 3*sqrt(2)/18
9sqrt(2)/18
sqrt(2)/2

The simplest form of the expression is sqrt(2)2.