Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Multiplication of surds

      Lesson details

      Learning outcome

      I can appreciate the structure that underpins multiplication of surds.

      Key learning points

      1. The square root operation is equivalent to the exponent 0.5 where the base is the term under the square root.
      2. You can deduce this as squaring and square rooting are inverse operations.
      3. Since the exponents for each term are the same, they can be combined.

      Keywords

      • Surd - A surd is an irrational number expressed as the root of a rational number.

      • Radical - The root sign is the radical symbol.

      • Radicand - The radicand is the value inside the radical symbol.

      Common misconception

      Pupils may not simplify after multiplying surds.

      Surds should always be written in their simplest form for the final answer.

      Teacher tip

      This lesson builds on the learning from arithmetic procedures: index laws (unit 4) which pupils should be familiar with before starting this lesson. It is suggested that this link is highlighted during the lesson to aid pupils in seeing connections.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      Three of the surds are like surds. Which one is not?

      $$\sqrt {48}$$
      $$2\sqrt {27}$$
      $$2\sqrt {12}$$
      Correct answer: $$2\sqrt {18}$$

      Q2.
      Three of the surds are like surds. Which one is not?

      $$-5\sqrt {80}$$
      Correct answer: $$-5\sqrt {30}$$
      $$a\sqrt {20}$$
      $$b\sqrt {45}$$

      Q3.
      $$10\sqrt {3} + a\sqrt {3} = -3\sqrt {3}$$. What is the value of $$a$$?

      Correct Answer: -13

      Q4.
      Simplify the expression $$\sqrt {12} + \sqrt {3} - \sqrt {27}$$

      $$3\sqrt {3} - \sqrt {27}$$
      $$-4\sqrt {3}$$
      $$6\sqrt {3}$$
      Correct answer: 0

      Q5.
      True or false? $$\sqrt {20}$$ and $$\sqrt {45}$$ are like terms.

      True
      Correct answer: False

      Q6.
      Simplify the expression $$2\sqrt {15} + 3\sqrt {20} - 7\sqrt {80}$$

      $$2\sqrt {15} - 100\sqrt {5}$$
      Correct answer: $$2\sqrt {15} - 22\sqrt {5}$$
      $$2\sqrt {15} - 4\sqrt {5}$$
      $$2\sqrt {15} - 2\sqrt {5}$$

      6 Questions

      Q1.
      Calculate $$\sqrt {99} \times \sqrt {99}$$

      Correct Answer: 99

      Q2.
      Calculate $$\sqrt {3.9} \times \sqrt {3.9}$$

      Correct Answer: 3.9

      Q3.
      When multiplying surds, we the radicands.

      Correct Answer: multiply, times

      Q4.
      Match up the multiplications with the simplied answers.

      Correct Answer:$$2\sqrt {6}$$,$$\sqrt {6} \times \sqrt {4}$$

      $$\sqrt {6} \times \sqrt {4}$$

      Correct Answer:30,$$3\sqrt {10}\times \sqrt {10}$$

      $$3\sqrt {10}\times \sqrt {10}$$

      Correct Answer:$$7\sqrt {2}$$,$$\sqrt {14} \times \sqrt {7}$$

      $$\sqrt {14} \times \sqrt {7}$$

      Correct Answer:$$3\sqrt {2}$$,$$\sqrt {3} \times \sqrt {6}$$

      $$\sqrt {3} \times \sqrt {6}$$

      Q5.
      When dividing surds we the radicands.

      Correct Answer: divide

      Q6.
      Simplify the following expression: $$\sqrt {12} \div \sqrt {3}$$

      Correct Answer: 2

      To help you plan your 10 maths lesson on: Multiplication of surds, download all teaching resources for free and adapt to suit your pupils' needs...