Higher only · surds

Surds.
Simplify, combine,
rationalise.

hunt for the
square number

a root that will not come out exactly —

Surd

√2, √3, √5 go on for ever

so leave them as roots: exact

step 1 of 4

Simplify a surd

1. Find the biggest square factor: 25.

2. Split the root. Root the square number.

✓ √50 = 5√2

√50

= √25 × 2 biggest square factor

= √25 × √2

= 5√2

step 2 of 4

Multiply surds

1. Multiply the numbers under the roots.

2. 36 is a square number, so it comes out.

✓ √a × √b = √ab

√3 × √12

= √36 multiply inside

= 6

step 3 of 4

Add like surds

1. Same surd: add the numbers in front.

2. Different surds stay separate.

✓ Simplify first: they may match

3√2 + 5√2

= 8√2 like 3x + 5x

√2 + √3 cannot combine

step 4 of 4

Rationalise

1. No surds allowed on the bottom.

2. Multiply top and bottom by the surd.

✓ √3 × √3 = 3

6√3

= 6√3 × √3√3that is × 1

= 6√33

= 2√3

surds —

Simplify

take out the biggest square

Multiply

multiply under the root

Rationalise

× top and bottom by the surd

Only like surds add:
treat √2 like x.

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