Surds

A self-marking exercise on calculating, simplifying and manipulating surds (radicals)

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Without using a calculator simplify the following. You can use the √ button to insert the root or radical symbol. You can earn a trophy if you get at least 9 questions correct and you do this activity online. Click the Help tab above for more information.

 1 $$\sqrt{4}$$ ☐ ☐ ✓ ✗ 2 $$\sqrt{18}$$ ☐ ☐ ✓ ✗ 3 $$\sqrt{75}$$ ☐ ☐ ✓ ✗ 4 $$\sqrt{20}$$ ☐ ☐ ✓ ✗ 5 $$\sqrt{180}$$ ☐ ☐ ✓ ✗ 6 $$\sqrt{294}$$ ☐ ☐ ✓ ✗ 7 $$\sqrt{252}$$ ☐ ☐ ✓ ✗ 8 $$\sqrt{35}$$ ☐ ☐ ✓ ✗ 9 $$\sqrt{144}$$ ☐ ☐ ✓ ✗ 10 $$\sqrt{490}$$ ☐ ☐ ✓ ✗ 11 $$\sqrt{396}$$ ☐ ☐ ✓ ✗ 12 $$\sqrt{87}$$ ☐ ☐ ✓ ✗
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This is Surds level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8

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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Sunday, March 15, 2020

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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

Level 8 - Finding the conjugate surd to rationalise the denominator

Paper Surprising Perimeter - A wonderful surds problem with a surprising result.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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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})

Help

The key properties you need are:

Examples

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

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

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

Answers should be given in their simplest form. For example:

$$\sqrt{3}-1$$ is simpler than $$-1+\sqrt{3}$$ as it uses less symbols.

$$\dfrac{5-\sqrt{3}}{2}$$ is simpler than $$\dfrac{\sqrt{3}-5}{-2}$$ as it uses less symbols.

Typing Mathematical Notation

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