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      Checking and securing understanding of roots and integer indices

      I can calculate with roots and integer indices, including estimating the answer.

      Lesson 5 of 11
      New
      New
      • Year 10

      Checking and securing understanding of roots and integer indices

      I can calculate with roots and integer indices, including estimating the answer.

      Lesson details

      Key learning points

      1. Integer indices state how often a number should be multiplied by itself.
      2. The square root of any perfect square will be an integer.
      3. The square root of any number can be found using a calculator but it may not be an integer.
      4. The square root of any number can be estimated by comparing the square roots of the closest perfect squares.

      Keywords

      • Indices - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).

      Common misconception

      Any number is a square or cube number because it can be squared or cubed.

      A square number is the result of a number being multiplied by itself. Emphasis must be on the result. A cube number is a number that has been multiplied by itself three times. Emphasis must be on the result of the repeated multiplication.

      When estimating the answer to a root of a number, pupils must know which square roots of a perfect square are either side of this number to make an estimate. For example, sqrt 15 is in-between sqrt 9 and sqrt 16. This can be a quick fire round.
      Teacher tip

      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

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      What is the lowest common multiple of 12 and 14?

      Correct Answer: 84

      Q2.
      What is the lowest common multiple of 12 and 15?

      Correct Answer: 60

      Q3.
      What is the lowest common multiple of 12 and 16?

      Correct Answer: 48

      Q4.
      What is the highest common factor of 12, 16 and 20?

      Correct Answer: 4

      Q5.
      What is the highest common factor of 12 and 18?

      Correct Answer: 6

      Q6.
      What is the highest common factor of 12 and 15?

      Correct Answer: 3

      Assessment exit quiz

      6 Questions

      Q1.
      Calculate $$10^2 + 5^2$$

      Correct Answer: 125

      Q2.
      Calculate $$9^2 + 3^3$$

      Correct Answer: 108

      Q3.
      Calculate $$6^2 + 3^4$$

      Correct Answer: 117

      Q4.
      What is the value of A for: $$10^2 + A^3 = 127$$

      Correct Answer: 3, A = 3

      Q5.
      What is the value of A for: $$A^2 + 6^3 = 360$$

      Correct Answer: 12, A=12

      Q6.
      Which is the best estimate for $$\sqrt{32}$$ (to 1 decimal place)?

      6.1
      5.3
      Correct answer: 5.7

      Lesson appears in

      UnitMaths / Arithmetic procedures: index laws