Square and Cube RootsFind square roots and cube roots by first calculating the prime factorisation of a number. 
This is level 1: find square roots of numbers up to 52² You will be awarded a trophy if you get at least 7 correct and you do this activity online.
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Factor Trees  Learn prime factorisation first.
Level 1  Find square roots of numbers up to 52²
Level 2  Find square roots of numbers up to 96²
Level 3  Find cube roots of the given numbers
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
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See the National Curriculum page for links to related online activities and resources.
Find the square root of 576
Begin by finding the prime factorisation of 576 either by using a Factor Tree or the following method:
$$\require{enclose} 2 )\enclose{bottom}{576} \\ 2 )\enclose{bottom}{288} \\ 2 )\enclose{bottom}{144} \\ 2 )\enclose{bottom}{72} \\ 2 )\enclose{bottom}{36} \\ 2 )\enclose{bottom}{18} \\ 3 )\enclose{bottom}{9} \\ 3 $$576 = 2^{6} × 3^{2}
This can be written as:
576 = ( 2^{3} × 3) × ( 2^{3} × 3)
So the square root of 576 is 2^{3} × 3 = 24
You may also want to use a calculator to check your working. See Calculator Workout skill 5.
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Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.
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