Free Printable Radicals and Special Right Triangles

1.

What is the correct formula to find the Leg of a 45-45-90 Triangle?

a)

Hypo = Leg $\times$ $\sqrt{2}$

b)

Leg = $\frac{Hypo}{\sqrt{2}}$

c)

LL = SL $\times$ 2

d)

Hypo = LL $\times$ 3

2.

What is the Pythagorean Theorem

a)

a²+ c² = b²

b)

a + b = c

c)

b² + c² = a²

d)

a² + b² = c²

3.

How do I find the Hypotenuse of a 45-45-90 Triangle

a)

Hypo = Leg $\times\sqrt{3}$

b)

$Hypo\ =\ Leg\ \times\sqrt{2}$

c)

$Leg\ =\ \frac{Hypo}{\sqrt{2}}$

d)

$SL\ =\frac{Hypo}{2}$

4.

Solve

\sqrt{20}

a)

$4\sqrt{5}$

b)

$2\sqrt{10}$

c)

$2\sqrt{5}$

d)

$4\sqrt{10}$

5.

Solve

\frac{2}{\sqrt{3}}

a)

$\frac{2}{3}$

b)

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

c)

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

d)

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

6.

How do I find the Hypotenuse of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{2}$

b)

$Hypo\ =\ SL\times2$

c)

$Hypo\ =Leg\ \times\sqrt{2}$

d)

$Hypo\ =\ LL\times\sqrt{3}$

7.

How do I find the Short Leg of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{2}$

b)

$Hypo\ =\ SL\times2$

c)

$Hypo\ =Leg\ \times\sqrt{2}$

d)

$SL\ =\ LL\times\sqrt{3}$

8.

How do I find the Long Leg of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{2}$

b)

$Hypo\ =\ SL\times2$

c)

$Hypo\ =Leg\ \times\sqrt{2}$

d)

$LL\ =\ SL\times\sqrt{3}$

9.

How do I find the Short Leg of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{\sqrt{2}}$

b)

$Hypo\ =\ SL\times2$

c)

$SL\ =\ \frac{LL}{\sqrt{3}}$

d)

$LL\ =\ SL\times\sqrt{3}$

10.

If the problem gives me the SL of a 30-60-90 Triangle, what two formulas will I use to solve the triangle?

a)

$Hypo\ =\ SL\ \times2$

b)

$Hypo\ =\ Leg\ \times\sqrt{2}$

c)

$LL\ =\ SL\ \times Hypo$

d)

$LL\ =\ SL\ \times\sqrt{3}$

11.

How do I find the Short Leg of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{2}$

b)

$SL\ =\ Hypo\times2$

c)

$SL\ =\ \frac{LL}{\sqrt{3}}$

d)

$SL\ =\ LL\times\sqrt{3}$

12.

Solve

\sqrt{64}

a)

$4\sqrt{5}$

b)

$8\sqrt{2}$

c)

$\sqrt{8}$

d)

8

13.

Solve

\sqrt{5}\times\sqrt{5}

a)

$\sqrt{5}$

b)

$5\sqrt{5}$

c)

25

d)

5

14.

Solve

2\sqrt{7}\times3

a)

$6\sqrt{7}$

b)

$5\sqrt{7}$

c)

$2\sqrt{21}$

d)

$3\sqrt{14}$

15.

How do I find the Short Leg of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{\sqrt{2}}$

b)

$Hypo\ =\ SL\times2$

c)

$SL\ =\ \frac{LL}{\sqrt{3}}$

d)

$LL\ =\ SL\times\sqrt{3}$

16.

How do I find the Long Leg of a 30-60-90 Triangle

a)

$LL\ =\ \frac{Hypo}{2}$

b)

$Hypo\ =\ LL\times2$

c)

$Hypo\ =Leg\ \times\sqrt{2}$

d)

$LL\ =\ SL\times\sqrt{3}$

17.

How do I find the Short Leg of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{2}$

b)

$Hypo\ =\ SL\times2$

c)

$Hypo\ =Leg\ \times\sqrt{2}$

d)

$SL\ =\ LL\times\sqrt{3}$

18.

How do I find the Hypotenuse of a 30-60-90 Triangle

a)

$SL\ =\ \frac{Hypo}{2}$

b)

$Hypo\ =\ SL\times2$

c)

$Hypo\ =Leg\ \times\sqrt{2}$

d)

$Hypo\ =\ LL\times\sqrt{3}$

19.

How do I find the Hypotenuse of a 45-45-90 Triangle

a)

Hypo = Leg $\times\sqrt{3}$

b)

$Hypo\ =\ Leg\ \times\sqrt{2}$

c)

$Leg\ =\ \frac{Hypo}{\sqrt{2}}$

d)

$SL\ =\frac{Hypo}{2}$

20.

What is the correct formula to find the Leg of a 45-45-90 Triangle?

a)

Hypo = Leg $\times$ $\sqrt{2}$

b)

Leg = $\frac{Hypo}{\sqrt{2}}$

c)

LL = SL $\times$ 2

d)

Hypo = LL $\times$ 3

21.

Solve

\frac{\sqrt{5}}{\sqrt{10}}

a)

$\frac{5\sqrt{5}}{10}$

b)

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

c)

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

d)

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

22.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

23.

√81

a)

12

b)

11

c)

10

d)

9

24.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

25.

Simplify the following radical: 2√24

a)

4√6

b)

2√6

c)

24√2

d)

4√4

26.

√5 × √10

a)

50

b)

2√5

c)

5√2

d)

5√10

27.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

28.

Simplify:

a)

1/5

b)

20/100

c)

2/10

d)

1/√25

29.

Simplify: √28 * √3

a)

√84

b)

2√21

c)

4√21

d)

2√7 * √3

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

Simplify:

a)

√12

b)

(4√3)/3

c)

√3

d)

(2√3)/3

34.

Simplify:

a)

√5

b)

(√14)/2

c)

√7

d)

Cannot be simplified

35.

Simplify:

a)

A

b)

B

c)

C

d)

D

36.

Simplify:

a)

A

b)

B

c)

C

d)

D

37.

Simplify:

a)

A

b)

B

c)

C

d)

D

38.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by √2

d)

Divide that leg by √2

39.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Isosceles

d)

Obtuse

40.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

41.

Find x.

a)

30°

b)

60°

c)

90°

d)

180°

42.

Find x.

a)

30°

b)

45°

c)

60°

d)

90°

43.

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.

44.

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

a)

4√2

b)

4

c)

8

d)

4√3

45.

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

46.

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

a)

8√2

b)

4√2

c)

4

d)

8

47.

Find the value of y.

a)

8

b)

4

c)

2√3

d)

8√3

48.

Find the value of y.

a)

7

b)

7√3

c)

14√3

d)

(14√3)/3

49.

Find the value of y.

a)

11√2

b)

11

c)

22

d)

(11√2)/2

50.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

Radicals and Special Right Triangles

Total questions: 50

Worksheet time: 2hrs 59mins

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