To rationalise 1/√3, multiply top and bottom by √3: √3/3. The value is unchanged because you multiplied by √3/√3 = 1.
When the denominator is like 1 + √10, multiply by its conjugate 1 − √10. The bottom becomes 1 − 10 = −9, because (a + b)(a − b) = a² − b². So 1/(1 + √10) = (1 − √10)/−9 = (√10 − 1)/9.
Worked example
Rationalise 2/(3 + √10).
- Multiply top and bottom by 3 − √10.
- Bottom: 9 − 10 = −1, so 2(3 − √10)/−1.
Answer:2√10 − 6
Key words
- rationalise
- make the denominator rational
- conjugate
- the same terms with the opposite sign in the middle
- difference of two squares
- (a + b)(a − b) = a² − b²
Practise this
New questions every time.
Common Core-referenced: HSN-RN.A.2