Free Printable Station #27 Rational Vs Irrational Numbers

1.

$\frac{\sqrt{4}}{6}$

a)

Rational

b)

Irrational

2.

$4.\overline{67}$

a)

Rational

b)

Irrational

3.

$\sqrt{49}$

a)

Rational

b)

Irrational

4.

$\sqrt{1000}$

a)

Rational

b)

Irrational

5.

$5.23568...$

a)

Rational

b)

Irrational

6.

$\sqrt{225}$

a)

Rational

b)

Irrational

7.

$\frac{2}{3}$

a)

Rational

b)

Irrational

8.

$\frac{\sqrt{9}}{\sqrt{16}}$

a)

Rational

b)

Irrational

9.

$0$

a)

Rational

b)

Irrational

10.

$-\sqrt{125}$

a)

Rational

b)

Irrational

11.

What kind of number is π ?

a)

rational

b)

irrational

c)

whole

d)

integer

12.

A REPEATING decimal is what type of number?

a)

Rational

b)

Irrational

13.

The square root of 2 is an irrational number because...

a)

All square roots are irrational

b)

The answer is a decimal that never stops

c)

Two is an even number

d)

The answer is 1

14.

Irrational numbers...

a)

reduce to π

b)

never end and never repeat

c)

can sometimes be perfect squares

d)

must be negative

15.

the product of $\sqrt{3\ \ }and\ \sqrt{9}$

a)

rational

b)

irrational

16.

the sum of $\sqrt{4\ \ }and\ \sqrt{9}$

a)

rational

b)

irrational

17.

the sum of $\sqrt{2\ \ }and\ \sqrt{5}$

a)

rational

b)

irrational

18.

the sum of $\sqrt{50\ \ }and\ \sqrt{9}$

a)

rational

b)

irrational

19.

the product of $\sqrt{50\ \ }and\ \sqrt{9}$

a)

rational

b)

irrational

20.

A perfect square is a number whose square root is ___________.

a)

Even

b)

irrational

c)

Rational

d)

Odd

21.

To find the square root of a number, you must divide it by 2.

a)

True

b)

False

22.

The √20 is between which two consecutive integers?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

23.

x² = 121
What does x equal?

a)

11²

b)

11 and -11

c)

20 and 11

d)

12 and 1

24.

What is the square root of 289?

a)

13

b)

140

c)

17

d)

18

25.

Which number has a square root that is between 7 and 8?

a)

48

b)

81

c)

60

d)

36

26.

17² =

a)

34

b)

289

c)

225

d)

324

27.

All the following are Perfect Squares except for which one?

a)

81

b)

121

c)

361

d)

198

28.

What is the area of a square with a side of 7?

a)

14

b)

28

c)

49

d)

64

29.

Square roots are the opposite of ____________.

a)

Cube Roots

b)

Squaring

c)

Multiplication

d)

Absolute Value

30.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

31.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

32.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

33.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

34.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

35.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

36.

What is one of the solutions to this equation?

(x - 3)² = 49

a)

7

b)

-7

c)

-4

d)

4

37.

Solve
a² + 10a + 21 = 0

a)

± √21

b)

-3 , -7

c)

3 , 7

d)

28 , -7

38.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

39.

Factor
x² + 4x + 3

a)

(x - 1)(x - 3)

b)

(x + 1)(x + 3)

c)

(x - 1)(x + 3)

d)

(x + 1)(x - 3)

40.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

Station #27 Rational Vs Irrational Numbers

Total questions: 40

Worksheet time: 53mins

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