Multiply and divide surds, square a surd term, and expand single and double brackets that contain surds.
What you will learn
- Multiply and divide surds
- Square a surd term
- Expand single and double brackets with surds
- Spot products where the surd cancels
Multiplying and dividing
A term is one part of a sum, joined to the rest by + or −: 4 − √3 has the terms 4 and −√3, and 2√5 on its own is one term.
- √a × √b = √(ab): √6 × √10 = √60 = 2√15.
- √a × √a = a: √7 × √7 = 7.
- Numbers in front multiply separately: 3√2 × 5√6 = 15√12 = 30√3.
- √a ÷ √b = √(a ÷ b): √72 ÷ √2 = √36 = 6.
- A product can come out whole: √12 × √3 = √36 = 6.
- Squaring a term squares both parts: (2√5)² = 2² × (√5)² = 4 × 5 = 20.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Multiplying and dividing
- Expanding brackets
- Try it: Expand, then check
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Expand
In this unit: Surds
Exact answers with square roots: simplifying, multiplying and expanding, rationalising denominators, and surds in Pythagoras and quadratics. Higher tier.
- Simplifying surds
- Multiplying and expanding surds
- Rationalising the denominator
- Exact answers with surds