Transum Software

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
No calculator

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.

$$\sqrt[2]{225}$$

Correct Wrong

$$\sqrt[2]{256}$$

Correct Wrong

$$\sqrt[2]{324}$$

Correct Wrong

$$\sqrt[2]{400}$$

Correct Wrong

$$\sqrt[2]{441}$$

Correct Wrong

$$\sqrt[2]{484}$$

Correct Wrong

$$\sqrt[2]{625}$$

Correct Wrong

$$\sqrt[2]{729}$$

Correct Wrong

$$\sqrt[2]{900}$$

Correct Wrong

Check

This is Square and Cube Roots level 1. You can also try:
Level 2 Level 3

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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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 self-marking 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.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

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.

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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