# Surds - Level 6

## 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 by first rationalising the denominator. You can use the √ button to insert the radical symbol.

 $$\frac{6}{\sqrt{2}}$$ $$\frac{12}{\sqrt{3}}$$ $$\frac{8}{\sqrt{4}}$$ $$\frac{10}{\sqrt{5}}$$ $$\frac{4\sqrt{6}}{\sqrt{2}}$$ $$\frac{5\sqrt{6}}{\sqrt{3}}$$ $$\frac{3\sqrt{12}}{\sqrt{4}}$$ $$\frac{3\sqrt{20}}{\sqrt{5}}$$ $$\frac{16\sqrt{3}}{4\sqrt{2}}$$ $$\frac{18\sqrt{2}}{3\sqrt{3}}$$ $$\frac{32\sqrt{2}}{4\sqrt{4}}$$ $$\frac{20\sqrt{4}}{2\sqrt{5}}$$

This is Surds level 6. 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.

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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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## 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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