# Surds - Level 3

## A self-marking exercise on calculating, simplifying and manipulating surds (also known as radicals).

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7Exam-StyleDescriptionHelp

Without using a calculator simplify the following. You can use the √ button to insert the radical symbol. You can earn a trophy if you get at least 9 questions correct and you do this activity online.

 $$4\sqrt{16} \times \sqrt{5}$$ $$4\sqrt{11} \times \sqrt{10}$$ $$\sqrt{15} \times 3\sqrt{12}$$ $$\sqrt{11} \times 4\sqrt{11}$$ $$7\sqrt{11} \times 3\sqrt{14}$$ $$5\sqrt{8} \times 7\sqrt{12}$$ $$(3 \sqrt{8})^2$$ $$(4 \sqrt{11})^2$$ $$(\sqrt[3]{10})^3$$ $$(\sqrt[4]{8})^4$$ $$(2\sqrt[3]{2})^3$$ $$(5\sqrt[4]{4})^4$$
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This is Surds level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7

## 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

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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Answer multiple choice questions about basic mathematical ideas. If you get a number of questions correct you will be invited to post a question of your own. The bank of questions grows larger every day.

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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.

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## 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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© Transum Mathematics :: This activity can be found online at:
wwww.Transum.org/go/?Num=3

## Description of Levels

Level 1 - Simplifying surds

Level 2 - Simplifying the product of two surds

Level 3 - Simplifying the product of integers and surds

Level 4 - Simplifying the sum of integers and surds

Level 5 - Simplifying fractions containing surds

Level 6 - Rationalising the denominator of a fraction

Level 7 - Miscellaneous questions involving surds

Exam Style questions are in the style of GCSE exam paper questions and worked solutions are available for Transum subscribers.

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.

There are three statements referring to surds in the English National Curriculum:

• Pupils should be taught to calculate exactly with fractions, {surds} and multiples of π ; {simplify surd expressions involving squares [for example √12 = √(4 × 3) = √4 × √3 = 2√3] and rationalise denominators}
• Pupils should be taught to simplify and manipulate algebraic expressions including those involving surds ...
• Pupils should be taught to recognise and use sequences ... and simple geometric progressions (rn where n is an integer, and r is a positive rational number {or a surd})

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The key properties you need are:

## Examples

$$\sqrt{80} = \sqrt{4\times4\times5} = \sqrt{4}\times\sqrt{4}\times\sqrt{5} = 2\times2\times\sqrt{5} = 4\sqrt{5}$$

$$\sqrt{8}\times\sqrt{12} = \sqrt{4\times2}\times\sqrt{4\times3} = 2\times\sqrt{2}\times2\times\sqrt{3} = 4\sqrt{6}$$

$$(5+\sqrt{7})(5-\sqrt{7}) = 25+5\sqrt{7}-5\sqrt{7}-7 = 25-7 = 18$$

This video is from UKMathsTeacher.

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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