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.
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.
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.
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can doubleclick the 'Check' button to make it float at the bottom of your screen.
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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