Square and Cube Roots

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Example

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 = 2⁶ × 3²

This can be written as:

576 = ( 2³ × 3) × ( 2³ × 3)

So the square root of 576 is 2³ × 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 double-click the 'Check' button to make it float at the bottom of your screen.

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$$\sqrt[2]{225}$$	$$\sqrt[2]{324}$$	$$\sqrt[2]{400}$$
$$\sqrt[2]{484}$$	$$\sqrt[2]{625}$$	$$\sqrt[2]{676}$$
$$\sqrt[2]{729}$$	$$\sqrt[2]{900}$$	$$\sqrt[2]{1156}$$

Square and Cube Roots

Find square roots and cube roots by first calculating the prime factorisation of a number.

Factor Trees Level 1 Level 2 Level 3 Description Help More Factors

Instructions

More Activities:

Featured Activity

Three Ways

Answers

Go Maths

Maths Map

Teachers

Description of Levels

Curriculum Reference

Example