CLASS 9 MATHS · NUMBER SYSTEMS

Rationalise the denominator

Multiply top and bottom by a surd that removes the root below: √a × √a = a and (√a + √b)(√a − √b) = a − b.

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Worked examples

Example 1 · level 1

Rationalise the denominator: 11/√2

22√2
11√2
11/2
11√2/2

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11/√2 × √2/√2 = 11√2/2.
Answer: 11√2/2.

Answer: 11√2/2

Example 2 · level 2

Rationalise the denominator: 1/(√11 − √3)

(√11 + √3)/8
√11 + √3
(√11 + √3)/14
(√11 − √3)/8

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Multiply by (√11 + √3)/(√11 + √3).
Denominator: (√11)² − (√3)² = 11 − 3 = 8.
Answer: (√11 + √3)/8.

Answer: (√11 + √3)/8

Example 3 · level 3

Rationalise the denominator: 1/(5 − √6)

(5 − √6)/19
(5 + √6)/31
(5 + √6)/19
(5 + √6)/25

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Multiply top and bottom by 5 + √6.
Denominator: 25 − 6 = 19.
Answer: (5 + √6)/19.

Answer: (5 + √6)/19