# Surds - Level 2

## A self-marking exercise on calculating with surds (also known as radicals).

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7DescriptionHelp

Without using a calculator simplify the following. You can use the √ button to insert the radical symbol.

 $$\sqrt{7} \times \sqrt{7}$$ $$\sqrt{9} \times \sqrt{9}$$ $$\sqrt{13} \times \sqrt{13}$$ $$\sqrt{2} \times \sqrt{8}$$ $$\sqrt{5} \times \sqrt{45}$$ $$\sqrt{4} \times \sqrt{64}$$ $$\sqrt{11} \times \sqrt{16}$$ $$\sqrt{16} \times \sqrt{14}$$ $$\sqrt{16} \times \sqrt{12}$$ $$\sqrt{14} \times \sqrt{7}$$ $$\sqrt{2} \times \sqrt{3}$$ $$\sqrt{5} \times \sqrt{9}$$

This is Surds level 2. You can also try:

## 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?

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

#### Online Logo

An opportunity for students to write a computer program. There is nothing to download, all of the interaction takes place in the browser. Great for understanding angles and the properties of shapes.

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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:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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## Description of Levels

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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

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.

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