Free Printable Extra Credit on Radicals A

1.

^{Find the missing side.}

^{Round to the nearest tenth if necessary.}

a)

29.2

b)

20

c)

400

d)

10

2.

Simplify:

\sqrt{80}

a)

$16\sqrt{5}$

b)

$2\sqrt{20}$

c)

$4\sqrt{5}$

d)

$8\sqrt{5}$

3.

Simplify:

\sqrt{x^8y^9}

a)

$x^4y^4\sqrt{y}$

b)

$x^8y^8\sqrt{y}$

c)

$x^2y^2\sqrt{y}$

d)

$x^4y^3$

4.

Simplify:

\sqrt{25x^6}

a)

$5x^2$

b)

$5x^3$

c)

$\sqrt{5x^3}$

d)

$5\sqrt{x^6}$

5.

Simplify:

\frac{\sqrt{7x^4y}}{\sqrt{5xy}}

a)

$2x^3$

b)

$\frac{x\sqrt{35x}}{5}$

c)

$\sqrt{2x^3}$

d)

$\frac{x\sqrt{35x}}{25}$

6.

Simplify:

\frac{\sqrt{7}}{\sqrt{2}}

a)

$\sqrt{5}$

b)

$\frac{\sqrt{14}}{2}$

c)

$\frac{\sqrt{7}}{2}$

d)

Cannot be simplified

7.

What type of number is $\pi$ ?

a)

rational

b)

irrational

c)

whole

d)

integer

8.

Simplify:

$\left(2\sqrt{75x^5y^3\ }\right)\ \left(4\sqrt{48xy}\right)$

a)

$240x^3y^2$

b)

$480x^3y^2$

c)

$240x^6y^4$

d)

$480x^6y^4$

9.

Simplify:

$\frac{6\sqrt{15x^5y^7}}{2\sqrt{3x^3y^4}}$

a)

$3xy\sqrt{5y}$

b)

$3xy\sqrt{15y}$

c)

$3\sqrt{5x^2y^3}$

d)

$3x^2y^2\sqrt{5y}$

10.

Simplify:

\sqrt{200x^2}

a)

$5x\sqrt{2}$

b)

$100x$

c)

$10x\sqrt{2}$

d)

$10\sqrt{2x}$

11.

Simplify:

5\sqrt{3}+\sqrt{12}

a)

$7\sqrt{3}$

b)

Can't Simplify

c)

$6\sqrt{15}$

d)

$9\sqrt{3}$

12.

Which one of the following numbers is NOT a Perfect Square?

a)

81

b)

121

c)

361

d)

198

13.

Simplify:

3\sqrt{2}-3\sqrt{18}

a)

$\sqrt{16}$

b)

$\sqrt{-16}$

c)

$-24\sqrt{2}$

d)

$-6\sqrt{2}$

14.

Simplify:

\left(\sqrt{2}-3\right)\left(8-\sqrt{2}\right)

a)

$5\sqrt{2}-22$

b)

$11\sqrt{2}-22$

c)

$5\sqrt{2}-26$

d)

$11\sqrt{2}-26$

15.

Find the product:

3\sqrt{6}\cdot2\sqrt{3}

a)

$6\sqrt{18}$

b)

$18\sqrt{2}$

c)

$54\sqrt{2}$

d)

$18\sqrt{3}$

16.

Simplify:

\frac{12}{\sqrt{15}}

a)

$\frac{12\sqrt{15}}{15}$

b)

$\frac{4\sqrt{15}}{5}$

c)

$\frac{4}{5}$

d)

Can't Simplify

17.

If the equal sides of an isosceles right triangle measure 12 units, then the measure of the hypotenuse is _____ units.

a)

$12\sqrt{2}$

b)

$4\sqrt{3}$

c)

$0$

d)

$144\sqrt{2}$

18.

Simplify:

\sqrt{10}\cdot\sqrt{45}

a)

$3\sqrt{50}$

b)

$\sqrt{55}$

c)

$\sqrt{450}$

d)

$15\sqrt{2}$

19.

Simplify:

6\sqrt{2}\cdot5\sqrt{14}

a)

$11\sqrt{28}$

b)

$60\sqrt{7}$

c)

$120\sqrt{7}$

d)

$30\sqrt{7}$

20.

Simplify:

\frac{4\sqrt{15}}{2\sqrt{6}}

a)

$2\sqrt{3}$

b)

$\sqrt{10}$

c)

$2\sqrt{10}$

d)

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

21.

Simplify:

\frac{\sqrt{49}}{\sqrt{84}}

a)

$\frac{\sqrt{21}}{6}$

b)

$\sqrt{21}$

c)

$\frac{\sqrt{7}}{2}$

d)

$\frac{7}{8}$

22.

Simplify:

\sqrt{4}\left(\sqrt{5}-3\sqrt{4}\right)

a)

$\sqrt{20}-3\sqrt{16}$

b)

$2\sqrt{5}-12$

c)

$\sqrt{20}-12$

d)

$2\sqrt{5}-48$

23.

Simplify:

\sqrt{12x^5}

a)

$6x^{2.5}$

b)

$2\sqrt{3x^5}$

c)

$2x^2\sqrt{3x}$

d)

$4x^2\sqrt{3x}$

24.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

25.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

26.

Which set of side lengths does NOT form a right triangle?

a)

24, 45, 51

b)

16, 63, 65

c)

36, 77, 85

d)

14, 15, 29

27.

^{Find the missing side.}

^{Round to the nearest tenth if necessary.}

a)

36

b)

76.8

c)

12

d)

40

28.

^{Find the missing side.}

^{Round to the nearest tenth if necessary.}

a)

37

b)

17.7

c)

6

d)

312

29.

Which equation can NOT be used to find the length of the missing side?

a)

12² + 13² = x²

b)

x² + 12² = 13²

c)

13² – 12² = x²

d)

13² – x² = 12²

30.

What is the length of the hypotenuse in the triangle shown?

a)

3

b)

4

c)

5

d)

7

31.

The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse?

a)

13

b)

14

c)

26

d)

34

32.

Simplify:

\sqrt{7}+\sqrt{7}

a)

$2\sqrt{7}$

b)

$\sqrt{14}$

c)

$\sqrt{49}$

d)

$7\sqrt{7}$

33.

Simplify:

\frac{4}{2-\sqrt{10}}

a)

$\frac{4}{2+\sqrt{10}}$

b)

$\frac{-4-2\sqrt{10}}{3}$

c)

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

d)

$\frac{4+2\sqrt{10}}{-6}$

34.

Simplify:

\left(3\sqrt{6}\right)^2

a)

$18$

b)

$54$

c)

$9\sqrt{36}$

d)

$3\sqrt{6}$

35.

If the diagonal of a square measures 10, find the AREA of the square.

a)

$50$

b)

$100$

c)

$20\sqrt{2}$

d)

$10\sqrt{2}$

36.

Simplify:

4\sqrt{50}-6\sqrt{2}

a)

$-2\sqrt{48}$

b)

$-8\sqrt{3}$

c)

$14\sqrt{2}$

d)

$26\sqrt{2}$

37.

Simplify:

2\sqrt{18}-\sqrt{72}

a)

$2\sqrt{-54}$

b)

$0$

c)

$\sqrt{2}$

d)

$12\sqrt{2}$

38.

Simplify:

\frac{\sqrt{108x^5y^8}}{\sqrt{6xy^5}}

a)

$\sqrt{18x^5y^3}$

b)

$3xy\sqrt{2y}$

c)

$3x^2y\sqrt{2y}$

d)

$3\sqrt{2x^4y^3}$

39.

Find the multiplicative inverse of:

9-\sqrt{6}

a)

$\frac{9+\sqrt{6}}{75}$

b)

$\frac{9-\sqrt{6}}{75}$

c)

$\frac{9+\sqrt{6}}{87}$

d)

$\frac{9-\sqrt{6}}{87}$

40.

What is the conjugate of:

5-\sqrt{2}

a)

$5+\sqrt{2}$

b)

$-5-\sqrt{2}$

c)

$-5+\sqrt{2}$

d)

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

Extra Credit on Radicals A

Total questions: 40

Worksheet time: 2hrs 26mins

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