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Simplifying surds
A surd is a square root that is not a whole number, like √2. Surds let you give exact answers instead of long decimals.
Split into a square number
√ab = √a × √b
Look for the biggest square factor: 4, 9, 16, 25, 36, 49...
√12 = √4 × √3 = 2√3
Look for the biggest square factor: 4, 9, 16, 25, 36, 49...
√12 = √4 × √3 = 2√3
Adding surds
Like surds add like algebra: 2√3 + 5√3 = 7√3
If the surds do not match, simplify them first and they often will.
If the surds do not match, simplify them first and they often will.
Rationalising the denominator
No surds on the bottom. Multiply top and bottom by the surd.
1√2 = √22 because √2 × √2 = 2
1√2 = √22 because √2 × √2 = 2
Simplify √50 + √18
- √50 = √25 × √2 = 5√2
- √18 = √9 × √2 = 3√2
- 5√2 + 3√2 = 8√2
Answer: 8√2
Find the biggest square factor and take its root outside. Only like surds can be added. To rationalise, multiply top and bottom by the surd.
Check you have got it
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