Examples for Rationalizing the Denominator

Examples

It is improper for a fraction to have a radical in its denominator.

To remove the radical we “rationalize the denominator”.

Examples for Rationalizing the Denominator (EX: 1 of 3)

n

n

n 8

8

8

7

264

56

n

n

n

n

8

142

n8

7

Next Example

n

n

4

14

n

n

8

144

Multiply numerator and denominator by the denominator

Simplify

Factors of 56. Simplify denominator.Take square root of 4 and write it outside the radical sign

Simplify…divide 2 and 8

Examples for Rationalizing the Denominator (EX: 2 of 3)

2

2

2 6

6

6

3

x

x

x

4

2

36

63

x

x

26

63

x

x

26

3

x

Next Example

x2

6

2

2

6

63

x

x

Multiply numerator and denominator by the denominator

Simplify

Simplify denominator.

Simplify the numerator.

Simplify the terms outside the radical sign.

Examples for Rationalizing the Denominator (EX: 3 of 3)

3

3

3

7

8

8

8

6320

y

y

y

y

6

10

64

50420

y

y

3

5

8

143620

y

y

3

7

8

7594

y

y3

10

8

50420

y

y

Multiply numerator and denominator by the denominator

Simplify

Simplify denominator.Break apart 504.

Take square root of y10 and write it outside the radical sign

Take square root of 36

3

7

8

6320

y

y Simplify

3

5

8

14620

y

y

3

5

8

14120

y

y

1415 2y

Simplify

Simplify