Free Printable Rationalizing Denominators and Conjugates Practice

1.

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)

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

2.

a)

b)

c)

d)

3.

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)

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

4.

Rationalize the Denominator:
$\frac{4}{3-\sqrt{2}}$

a)

$\frac{12+4\sqrt{2}}{7}$

b)

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

c)

$\frac{12-2\sqrt{2}}{3}$

d)

$\frac{4-12\sqrt{2}}{7}$

5.

What is the conjugate of:
$5+\sqrt{7}$

a)

18

b)

$5+\sqrt{7}$

c)

$5-\sqrt{7}$

d)

32

6.

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)

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

7.

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

a)

$16-\sqrt{2}$

b)

$4-\sqrt{2}$

c)

14

d)

18

8.

Rationalize the denominator:
$\frac{\sqrt{4}}{\sqrt{121}}$

a)

$\frac{4}{11}$

b)

$\frac{\sqrt{484}}{121}$

c)

$\frac{2}{11}$

d)

$\frac{2\sqrt{121}}{121}$

9.

Divide:
$\frac{10\sqrt{30}}{\sqrt{15}}$

a)

$\frac{2\sqrt{30}}{3}$

b)

$10\sqrt{2}$

c)

20

d)

$2\sqrt{10}$

10.

Which is the conjugate of $-2\sqrt{x}+5\sqrt{x-1}$

a)

$-2\sqrt{x}-5\sqrt{x+1}$

b)

$-2\sqrt{x}-5\sqrt{x-1}$

c)

$2\sqrt{x}-5\sqrt{x-1}$

d)

$2\sqrt{x}+5\sqrt{x+1}$

Rationalizing Denominators and Conjugates Practice

Total questions: 10

Worksheet time: 10mins

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