Free Printable Surds

1.

Rationalise the Denominator:
^{(3 + √4)}/_√2

a)

^5√2/₂

b)

^{(3√2 +√8)}/₂

c)

^{(3√2 +√8)}/4

d)

^{(3√2 +}^√3⁾/₂

2.

Fully simplify...

a)

b)

c)

d)

3.

Fully simplify...

a)

b)

c)

d)

4.

Simplify fully:
2√45 - 5√45 + 9√16

a)

-9√5 + 36

b)

-3√45 + 144

c)

6√16

d)

6√106

5.

Expand and simplify.....

√5(1 - √3)

a)

√5 - √15

b)

1√5 - 3√5

c)

√5 - 3√5

d)

√5 - 5√3

6.

Rationalize the denominator: $\frac{5+x}{2x-\sqrt{3x}}$

a)

$\frac{10x+5x\sqrt{3x}+2x^2}{7x}$

b)

$\frac{10x+5\sqrt{3x}+2x^2+x\sqrt{3x}}{x}$

c)

$\frac{10x+5x\sqrt{3x}+2x^2}{4x^2-3x}$

d)

$\frac{10x+5\sqrt{3x}+2x^2+x\sqrt{3x}}{4x^2-3x}$

7.

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

a)

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

b)

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

c)

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

d)

$-2\sqrt{6}$

8.

What is the conjugate of:
$-3\sqrt{2}-6$

a)

$-3\sqrt{2}+6$

b)

$3\sqrt{2}+6$

c)

$-6-3\sqrt{2}$

d)

$-2\sqrt{3}-6$

9.

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

10.

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)

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

11.

Multiply:
$\left(4+\sqrt{2}\right)\left(4-\sqrt{2}\right)$

a)

$16-\sqrt{2}$

b)

$4-\sqrt{2}$

c)

14

d)

18

12.

What is the conjugate of:
$6-3\sqrt{2}$

a)

$6+3\sqrt{2}$

b)

$3\sqrt{2}+6$

c)

$6-3\sqrt{2}$

d)

18

13.

Rationalize the denominator:
$\frac{2\sqrt{8}}{\sqrt{12}}$

a)

$\frac{\sqrt{96}}{6}$

b)

$\frac{2\sqrt{6}}{3}$

c)

$\frac{2\sqrt{96}}{12}$

d)

$\frac{4\sqrt{2}}{2\sqrt{3}}$

14.

Rationalize the denominator:
$\frac{\sqrt{5}}{2\sqrt{3}}$

a)

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

b)

$\frac{\sqrt{15}}{18}$

c)

$\frac{5\sqrt{3}}{6}$

d)

$\frac{5\sqrt{3}}{18}$

15.

Simplify √288

a)

144

b)

12√2

c)

3√32

d)

144√2

16.

Simplify fully:
√120

a)

4√30

b)

2√30

c)

12√10

d)

6√10

17.

$5\ \sqrt[]{20}\times4\ \sqrt[]{80}$

a)

400

b)

$10\ \sqrt[]{20}$

c)

200

d)

800

18.

Expand and simplify ...

(2 + √3)(1 + √3)

a)

5 + 3√3

b)

2 + 3√3

c)

5 + √3

d)

11 + 3√3

19.

Simplify fully:
2√45 - 5√45 + 9√16

a)

-9√5 + 36

b)

-3√45 + 144

c)

6√16

d)

6√106

20.

$2√32-√50+√98$

a)

$√2$

b)

$10√2$

c)

$56√2$

d)

$700√2$

Surds

Total questions: 20

Worksheet time: 30mins

Similar Resources on Wayground