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Surds - Level 7

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

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Description Help

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

$$\frac{15}{\sqrt{5}}-\sqrt{20}$$

Correct Wrong

$$\frac{12}{\sqrt{3}}-\sqrt{27}$$

Correct Wrong

$$\sqrt{3}+\sqrt{27}-\sqrt{12}$$

Correct Wrong

$$\frac{6}{\sqrt{2}}+\frac{12}{\sqrt{6}}$$

Correct Wrong

$$\frac{15}{\sqrt{3}}+\frac{30}{\sqrt{5}}$$

Correct Wrong

$$(2\sqrt{3})^6$$

Correct Wrong

$$(\sqrt{14}+1)(\sqrt{14}-1)$$

Correct Wrong

$$(\sqrt{15}+2)(\sqrt{15}-2)$$

Correct Wrong

$$(\sqrt{17}+3)(\sqrt{17}-3)$$

Correct Wrong

$$\frac{12}{3+\sqrt{3}}$$

Correct Wrong

$$\frac{30}{3+\sqrt{3}}$$

Correct Wrong

$$\frac{93}{6+\sqrt{5}}$$

Correct Wrong

This is Surds level 7. 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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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:

Surds

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.

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