Surds: Rationalising The Denominator

Question 1

What does rationalising the denominator mean?

Answer 1

Rationalising the denominator means we want to make the denominator a whole number and not a surd. Making an equivalent fraction but where there’s not a surd at the bottom.

Question 2

Rationalise the denominator of 3 / √5

Answer 2

3 x √5 = 3√5
— = 3√5 / 5
√5 x √5 = 5

Question 3

Rationalise the denominator of

3
—
√b

Giving your answer in the form where a and b are integers

√a
—
b

Answer 3

3 x √6
— = 3√6 / 6
√6 x √6

3√6 ÷ 3
—— = √6 / 2
√6 ÷ 3

We are diving by 3 to get it into the form the questions asked for.

Question 4

Rationalise

3 + √5
——–
2√5

Answer 4

3 + √5 x √5
——– = 3√5 + 5 / 10
2√5 x √5

Question 5

Rationalise

  12      ———— 1 / √5 + 5

Answer 5

12 x √5
————
1 / √5 + 5 x √5

=

12√5 ————–       √5 / √5 + 5 = 1 + 5 = 6

=

12√5
——– = 2√5
6

Question 6

Rationalise the denominator of

3
——-
2 - √5

Answer 6

6 + 3√5
————
-1

Or you could write:

-6 - 3√5