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Grade 7 · Higher · free GCSE maths worksheet

Simplifying surds

Writing root 50 as 5 root 2.

10 original questions, 26 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write √50 in the form a√2, where a is an integer.

1 mark
Show answer
5√2
2

Write √6 × √3 in the form a√2, where a is an integer.

2 marks
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3√2
3

Work out √72 ÷ √2.

2 marks
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6
4

Show that √12 + √27 can be written as 5√3.

2 marks
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2√3 + 3√3 = 5√3
5

Express √80 + √45 in the form k√5, where k is an integer.

3 marks
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7√5
6

Write 8√3 in the form √n, where n is an integer.

2 marks
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√192
7

Expand and simplify (3 + √2)(1 + √2). Give your answer in the form a + b√2.

3 marks
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5 + 4√2
8

Show that √50 + 18√2 = 14√2

5 marks
Show answer
√50 = 5√2 and 18√2 = 9√2, so the sum is 14√2
9

A right-angled triangle has hypotenuse 10 cm. One of the other sides is 2√7 cm.

Work out the length of the third side. Give your answer in the form k√2, where k is an integer.

3 marks
Show answer
6√2 cm
10

A rectangle has length 2√6 cm and width 3√2 cm.

Work out the area of the rectangle. Give your answer in the form k√3.

3 marks
Show answer
12√3 cm²

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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