Free Printable Operations on Surds and Radicals

1.

Simplify fully:
√120

a)

4√30

b)

2√30

c)

12√10

d)

6√10

2.

Simplify

a)

13√3

b)

10√30

c)

13√6

d)

11√3

3.

2√5 - √5 + 4√5 + √3

a)

6√5 + √3

b)

5√5 + √3

c)

6√5

d)

6√3

4.

Simplify the following surd...

a)

10√2

b)

8√2

c)

2√8

d)

5√8

5.

Fully simplify....

a)

b)

c)

d)

6.

Fully simplify...

a)

b)

c)

d)

7.

Fully simplify...

a)

b)

c)

d)

8.

Fully simplify...

a)

b)

c)

d)

9.

Simplify $\frac{3\sqrt{8}}{5\sqrt{200}}$

a)

$\frac{3\sqrt{2}}{25}$

b)

$\frac{6\sqrt{2}}{15\sqrt{2}}$

c)

$\frac{3}{25}$

d)

$\frac{3}{5}$

10.

Expand and simplify $\left(8-\sqrt{6}\right)\left(8+\sqrt{6}\right)$

a)

$2\sqrt{2}$

b)

$70$

c)

$58$

d)

$-70$

11.

Expand and simplify fully $\left(2+\sqrt{7}\right)\left(1+\sqrt{7}\right)$

a)

$9+\sqrt{7}$

b)

$9+3\sqrt{7}$

c)

$2+\ 3\sqrt{7}+7$

d)

$2+\sqrt{7}$

12.

The area of a rectangle is $3\ cm^2$ . The length of one side of the rectangle is $\sqrt{7}$ . In the e simplest form, what is the length of the other side.

a)

$3\sqrt{7}$

b)

$\frac{3}{\sqrt{7}}$

c)

$\frac{3\sqrt{7}}{7}$

d)

$\frac{\sqrt{7}}{3}$

13.

What should you multiply $\frac{6}{1-\sqrt{5}}$ by to rationalize the denominator?

a)

-4

b)

$1-\sqrt{5}$

c)

$1+\sqrt{5}$

d)

$-\frac{\left(3-3\sqrt{5}\right)}{2}$

14.

What is the conjugate of:
$4\sqrt{2}-\sqrt{5}$

a)

$4\sqrt{2}+\sqrt{5}$

b)

$\sqrt{5}+4$

c)

$4\sqrt{2}-\sqrt{5}$

d)

27

15.

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$ by to rationalize the denominator?

a)

$2-\sqrt{7}$

b)

$\sqrt{7}$

c)

$2+\sqrt{7}$

d)

$\sqrt{2}$

16.

5√2 x 2√3

a)

10√6

b)

6√10

c)

60

d)

15√6

17.

What is a surd?

a)

A recurring decimal

b)

An irrational number

c)

A fraction

d)

A rational number

18.

Select a surd.

a)

√2

b)

√4

c)

√99

d)

√20

19.

What should you multiply $\frac{3\sqrt{2}}{2-\sqrt{7}}$ by to rationalize the denominator?

a)

$2-\sqrt{7}$

b)

$\sqrt{7}$

c)

$2+\sqrt{7}$

d)

$\sqrt{2}$

20.

$\frac{-2}{1+\sqrt{6}}$ Rationalize the following:

a)

$\frac{1+\sqrt{6}}{-2}$

b)

$\frac{-2+2\sqrt{6}}{-5}$

c)

$-\frac{2\sqrt{6}}{6}$

d)

$-2\sqrt{6}$

21.

a)

$2\sqrt{2}cm$

b)

$\sqrt{8}\ cm$

c)

$\sqrt{27}cm$

d)

$3\sqrt{3}cm$

22.

Calculate the perimeter of the rectangle shown. give your answer in a simplified surd form.

a)

$4\sqrt{10}\ cm$

b)

$2\sqrt{5}\ cm$

c)

$5\sqrt{2}\ cm$

d)

$3\sqrt{5}\ cm$

23.

Calculate the value of x for the right angled triangle shown.

a)

$\sqrt{24}$

b)

$\sqrt{42}$

c)

$\sqrt{1024}$

d)

$\sqrt{54}$

24.

Calculate the value of x for the right angled triangle shown.

a)

100 cm

b)

10 cm

c)

$2\sqrt{5}\ cm$

d)

$5\sqrt{2}\ cm$

25.

a)

a = -4, b = 5

b)

a = 7, b = 3

c)

a = -4, b = 7

d)

a = 4, b = -5

Operations on Surds and Radicals - Grade 10 Practice.

Total questions: 25

Worksheet time: 33mins

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