Simplifying surds
The Maths Habit
True or false?
√4 × √9 = √36True: 2 × 3 = 6
√9 + √16 = √25False: 3 + 4 = 7
What is the largest square factor?
12
450
2572
3698
49
- Surd
- A root that does not come out as a whole number.
A square has an area of 20 cm². How long is each side?
Cut it into 4 equal squares. How long is each small side?
5 cm² each, so each small side is √5 cm
The big side is two small sides.
√20 = 2√5
The quick way: 20 is 4 lots of 5.
√20 = √4 × √5 = 2 × √5 = 2√5
√4 = 2: the 4 squares make 2 along each side.
Simplify √20.
√20=√4×√5
square root of the square number
=2×√5
Answer2√5
Simplify √28.
√28=√4×√7
square root of the square number
=2×√7
Answer2√7
Simplify √20.
√20=√4×√5
square root of the square number
=2×√5
Answer2√5
Simplify √63.
√63=√9×√7
square root of the square number
=3×√7
Answer3√7
Simplify √12 + √27.
5√3A square has an area of 48 cm². Write its side length in the form a√3.
4√3 cm
