Free Printable Unit 8 Lesson 6: Operations with Radical Expressions

1.

Simplify.
$\sqrt{12}+\sqrt{48}-\sqrt{27}$

a)

$3\sqrt{3}$

b)

$3\sqrt{9}$

c)

$9\sqrt{3}$

d)

$-24\sqrt{3}$

2.

Simplify.
$\sqrt{98}-\sqrt{72}+\sqrt{32}$

a)

$5\sqrt{2}$

b)

$17\sqrt{2}$

c)

$5\sqrt{6}$

d)

$-168\sqrt{2}$

3.

Simplify.
$\left(5+\sqrt{6}\right)\left(5-\sqrt{2}\right)$

a)

$25-5\sqrt{2}+5\sqrt{6}-2\sqrt{3}$

b)

$25-2\sqrt{2}$

c)

$\sqrt{25}-5\sqrt{2}+5\sqrt{6}-2\sqrt{3}$

d)

$25-2\sqrt{3}$

4.

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

a)

$5-2\sqrt{6}$

b)

$5$

c)

$13$

d)

$-1-2\sqrt{6}$

5.

Simplify.
$5+6\sqrt{7}-2\sqrt{7}-3$

a)

$2+4\sqrt{7}$

b)

$2+4\sqrt{14}$

c)

$2-12\sqrt{7}$

d)

$6$

6.

Simplify.
$6\sqrt{40}-3\sqrt{10}$

a)

$9\sqrt{10}$

b)

$-\sqrt{10}$

c)

$9\sqrt{100}$

d)

$5\sqrt{10}$

7.

Simplify.
$\sqrt{200}\cdot\sqrt{18}$

a)

$13\sqrt{2}$

b)

$30\sqrt{2}$

c)

$13\sqrt{4}$

d)

$26$

8.

Simplify.
$\sqrt{3}\cdot\sqrt{6}$

a)

$3\sqrt{2}$

b)

$2\sqrt{3}$

c)

$\sqrt{18}$

d)

$9\sqrt{2}$

9.

Simplify.
$\left(3-\sqrt{2}\right)\left(4+\sqrt{2}\right)$

a)

$10-\sqrt{2}$

b)

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

c)

$10-\sqrt{4}$

d)

$10+\sqrt{2}$

10.

Simplify.
$\left(2+\sqrt{3}\right)^2$

a)

$7+4\sqrt{3}$

b)

$7$

c)

$4+\sqrt{9}$

d)

$7+4\sqrt{6}$

11.

Find the perimeter of a square whose sides measure $\left(2\sqrt{3}+3\sqrt{12}\right)$ feet.

Hint: All sides are the same on a square.

a)

$32\sqrt{3}$ feet

b)

$8\sqrt{3}+12\sqrt{12}$ feet

c)

$11\sqrt{3}$ feet

d)

$12\sqrt{3}+8\sqrt{12}$ feet

12.

Find the area of a rectangle with side lengths $2\sqrt{15}$ and $4\sqrt{21}$ .

a)

$24\sqrt{35}$ square feet

b)

$8\sqrt{315}$ square feet

c)

$\sqrt{315}$ square feet

d)

$3\sqrt{35}$ square feet

Unit 8 Lesson 6: Operations with Radical Expressions

Total questions: 12

Worksheet time: 6mins

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