# Square and Cube Roots

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

##### Factor TreesLevel 1Level 2Level 3DescriptionHelpMore Factors

This is level 3: find cube roots of the given numbers You will be awarded a trophy if you get at least 7 correct and you do this activity online.

 $$\sqrt[3]{2744}$$ $$\sqrt[3]{4096}$$ $$\sqrt[3]{5832}$$ $$\sqrt[3]{10648}$$ $$\sqrt[3]{13824}$$ $$\sqrt[3]{17576}$$ $$\sqrt[3]{21952}$$ $$\sqrt[3]{32768}$$ $$\sqrt[3]{35937}$$
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This is Square and Cube Roots level 3. You can also try:
Level 1 Level 2

## 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.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

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The classic problem of using two unmarked jugs to measure exactly a given quantity. The Transum version is interactive and awards a virtual trophy for each of the levels completed.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Scan the QR code below to visit the online version of this activity.

Transum.org/go/?Num=836

## 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.

## Curriculum Reference

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

## Example

Find the cube root of 5832

Begin by finding the prime factorisation of 5832 either by using a Factor Tree or the following method:

$$\require{enclose} 2 )\enclose{bottom}{5832} \\ 2 )\enclose{bottom}{2916} \\ 2 )\enclose{bottom}{1458} \\ 3 )\enclose{bottom}{729} \\ 3 )\enclose{bottom}{243} \\ 3 )\enclose{bottom}{81} \\ 3 )\enclose{bottom}{27} \\ 3 )\enclose{bottom}{9} \\ 3$$

5832 = 23 × 36

This can be written as:

5832 = ( 2 × 32) × ( 2 × 32) × ( 2 × 32)

So the cube root of 5832 is 2 × 32 = 18

You may also want to use a calculator to check your working. See Calculator Workout skill 7.

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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