Free Printable Ch 6.1 Review

1.

In this 45-45-90 triangle, if the length of one leg is 5 units find the other leg.

a)

Multiply that leg by 2, so y=10

b)

Use the same length for the given leg to find y, so y=5

c)

Multiply that leg by √2, so y=5√2

d)

Divide that leg by √2, so y= 5/√2

2.

In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?

a)

It is the same length as the given leg.

b)

Multiply that leg's length by √2.

c)

Multiply that leg's length by 2.

d)

Divide that leg's length by √2.

3.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

4.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

5.

Which side is the long leg in this 30-60-90 triangle?

a)

4

b)

u

c)

v

6.

Which side is the short leg of this 30-60-90 triangle?

a)

6

b)

m

c)

n

7.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

8.

I have been given the short leg in this 30-60-90 triangle. How do I find the length of the hypotenuse?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by √3

9.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

10.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

11.

Find the value of y.

a)

7

b)

7√3

c)

14√3

d)

(14√3)/3

12.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

13.

A square tablecloth has a line of embroidered flowers along the diagonal. The tablecloth is 48 in. on each side. How long is the embroidery line? Round to the nearest inch.

a)

48√2

b)

68

c)

34

d)

24√2

14.

A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

a)

134.4

b)

67.2

c)

95√2

d)

(95√2)/2

15.

A square has diagonal length 13 m. What is the side length of the square, to the nearest centimeter?

a)

9.19

b)

18.38

c)

5.10

d)

13

16.

An equilateral triangle has height 26 cm. What is the length of each side of the triangle, to the nearest centimeter?

a)

26, 13, 23

b)

26, 26, 38

c)

26, 15, 30

d)

26, 42, 38

17.

Multiply $5\sqrt{2}\cdot\sqrt{2}$ .

(a)

18.

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

a)

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

b)

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

c)

$4\sqrt{3}$

19.

What type of special right triangle is this?

a)

Isoceles right

b)

30-60-90

c)

not a special right triangle

20.

What type of special right triangle is this?

a)

Isoceles right

b)

30-60-90

c)

not a special right triangle

21.

What type of special right triangle is this?

a)

45-45-90

b)

30-60-90

c)

not a special right triangle

22.

How long is e?

a)

3

b)

6

c)

$6\sqrt{3}$

d)

$6\sqrt{2}$

23.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

24.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

25.

Write as a radical expression
y¹⁄ ³

a)

∛y

b)

y³

c)

√y

d)

1∕ 3y

26.

Simplify:

a)

2

b)

8

c)

16

d)

32

27.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

28.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

29.

Write in exponential form
√x⁵

a)

X¹∕ ⁵

b)

X ²⁄⁵

c)

X⁵⁄ ²

d)

X⁵

30.

Write in exponential form
∜(3x)³

a)

3x³⁄ ⁴

b)

(3x)³∕ ⁴

c)

(3x)⁴⁄ ³

d)

3x⁴⁄ ³

31.

Write as a radical expression
y²⁄ ³

a)

2y³

b)

√y³

c)

∛y²

d)

3y²

32.

Simplify
x²⁄ ³⋅x¹⁄ ³

a)

2x

b)

x²⁄₉

c)

x

d)

x²

33.

Simplify
(x²⁄ ³)²⁄ ⁵

a)

x⁴∕ ¹⁵

b)

x¹⁶∕ ¹⁵

c)

x⁶

d)

6x

34.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

35.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

36.

Simplify √48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

37.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

38.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

39.

Which expression is equivalent to (x³y)⁶

a)

2x¹⁸y⁶

b)

x¹⁸y⁶

c)

x³y⁶

d)

x³y⁶

40.

100^1/2 = ?

a)

50

b)

10

c)

100.5

d)

20

41.

Simplify and evaluate $\left(5^2\right)^{\frac{3}{2}}$

a)

$5^3=125$

b)

$5^{\frac{3}{4}}$

c)

$5^6=\ 15,625$

d)

$3$

42.

Simplify:

a)

8x⁹

b)

8x³

c)

8x⁴√x

d)

8x³√x

43.

Simplify
(6^3/4)^1/3

a)

6^1/4

b)

6^3/12

c)

6^4/7

d)

6^9/12

44.

Write the expression in simplest form.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

45.

$\left(12^3x^{-7}y^4m\right)^0$

a)

$12^3\cdot\frac{1}{x^7}\cdot y^4\cdot m$

b)

1

c)

0

d)

$12x^{-7}y^4m$

46.

13

\frac{^3\sqrt{80}}{^3\sqrt{10}}=^3\sqrt{\frac{80}{10}}=2

a)

True

b)

False

47.

According to exponent rules, when we divide the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

48.

$\left(\frac{3x^4}{y^{-2}}\right)^5=?$

a)

$3^5x^9y^{-7}$

b)

1

c)

$\frac{3^5x^{20}}{y^{-10}}=3^5x^{20}y^{10}$

d)

$3^5x^{20}y^{-10}$

Ch 6.1 Review

Total questions: 48

Worksheet time: 1hrs 9mins

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