Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 41: Rationalizing Denominators and Numerators
of Radical Expressions

WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 41: Rationalizing Den and Num of Radical Expressions

Answer/Discussion to 1a

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

Since we have a square root in the denominator, we need to multiply by the square root of an expression that will give us a perfect square under the square root in the denominator.

So in this case, we can accomplish this by multiplying top and bottom by the square root of 11:

*Mult. num. and den. by sq. root of 11

*Den. now has a perfect square under sq. root

Step 2: Make sure all radicals are simplified

AND

Step 3: Simplify the fraction if needed.

*Sq. root of 121 is 11

(return to problem 1a)

Answer/Discussion to 2a

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the numerator.

Since we have a cube root in the numerator, we need to multiply by the cube root of an expression that will give us a perfect cube under the cube root in the numerator.

So in this case, we can accomplish this by multiplying top and bottom by the cube root of :