Estimating powers and roots

Sample Estimating powers and roots questions

A few of the 23 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 11 markGrade 3
   Which number is closest to the value of $29^3$? 27000, 90, 2700, 9000
   Show the worked solution

   29 is close to 30, and 30³ = 27,000. This is much closer than the other options, and indeed 29³ = 24,389, closest to 27,000.
2. Question 22 marksGrade 5
   Show that 268 can be written as the sum of a power of 3 and a square number.
   Show the worked solution

   Try 3⁵ = 243. 268 − 243 = 25 = 5², which is a square number. M1

What are the common mistakes in Estimating powers and roots?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Estimates a square/cube root by halving the target number instead of testing nearby values

  Halved 127 instead of finding the nearest perfect squares either side of it

• Miscounts by one when listing or bracketing cube numbers

  Used 2³ and 3³ as the bracketing cubes, but 3³ = 27 is still below 37 - the correct bracket is 3 and 4

• Miscounts by one when listing or bracketing square numbers

  Used 10² and 11² as the bracketing squares, but 11² = 121 is still below 127 - the correct bracket is 11 and 12

Quick answers about Estimating powers and roots

How many Estimating powers and roots practice questions are there?

There are 23 self-marking GCSE Maths questions on Estimating powers and roots, written for AQA, Pearson, OCR across Higher tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Estimating powers and roots?

No. You can start practising Estimating powers and roots straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.