Show:
Rational or Irrational?
Location of Roots
Product OR Power
Quotient OR Negative
Ordering the "Mess"
100

Is the number 2.121121112... rational or irrational?

Irrational (It is a non-terminating, non-repeating decimal).

100

The value of

sqrt 85

 is between which two consecutive integers?

9 and 10 (Because

sqrt 81 =9

sqrt 100 = 10

100

Simplify: 

a^4*a^3

a^7

100

Simplify:

x^9/x^4

x^5

(Subtract exponents)

100

Which is greater: 32 or 23?

32 (9 is greater than 8).

200

Which of these is rational:

pi/4

or

sqrt 144/ sqrt 100

sqrt 144/ sqrt 100 12/10 or 1.2

because it simplifies to

200

If you are plotting

-sqrt 17

 on a number line, between which two integers would you place a dot?

Between -4 and-5 (Because

sqrt 16 =4

, so

-sqrt 17

 is just past -4).

200

Simplify the coefficients (numbers) only:

4x^2*3x^5

12 (Because 4 x 3 = 12)

200

Simplify:10x5 / 2x2

5x3 (Divide numbers, subtract exponents)

200

Arrange from least to greatest:

5.1, 4.9, sqrt 25

4.9, sqrt 25=5, 5.1

300

True or False: The set {3, 2, 1, -0.75,

pi

} consists only of rational numbers.

False (Because

pi

 is irrational)

300

Is

sqrt 50

 closer to 7 or 8?

7. (It is very close to

sqrt 49

300

Simplify the variables only:

4x^2*3x^5

x^7

(Because 2 + 5 = 7).

300

Rewrite

5^-2

 without a negative exponent

1/5^2 OR 1/25

300

Which list is in order from least to greatest?

  • A)

    sqrt{10}, 3.5, \pi

  • B) 

    \pi, \sqrt{10}, 3.5

B (\pi \approx 3.14, \sqrt{10} \approx 3.16, 3.5)

400

Why can the value of

pi

 not be written as a ratio of two integers?

Because it is an irrational number (or: its decimal expansion never terminates or repeats)

400

Which point on a number line best represents

sqrt 8

?

  • A) Exactly on 3

  • B) A little less than 3

  • C) A little more than 2

B (A little less than 3, since

sqrt 9 = 3


400

Simplify completely:

(3y^2)^3

27y^6

(Cube the 3 to get 27, multiply 2 x 3 for the exponent).

400

Simplify to a single positive exponent: 4y2 /4y6

1/y^4

400

Place the following in order from least to greatest: 

4, \sqrt{15}, and 3.5


  • 3.5, \sqrt{15}, 4

    Explanation: 3.5 is the smallest.

    \sqrt{15}

     is just under 4 (approx 3.87). 4 is the largest.

500

Identify the irrational number in this list: 

sqrt 100, sqrt 18, 0.333..., -5

sqrt 18

(It is not a perfect square)

500

How much greater is

sqrt 26

 than

sqrt 17

?

  • A) Exactly 9

  • B) Less than 1

  • C) A little more than 1

B (Less than 1.

sqrt 26

 

~~

5.1 and

sqrt 17

~~

4.1. The gap between roots shrinks as numbers get higher)

500

Find the error: A student simplified

(2x^5)^2

 and got

4x^7

. What did they do wrong?

They added the exponents (5+2) instead of multiplying them (5 x 2). The correct answer is

4x^10

500

Simplify completely: -20a6b3/5a2b

-4a4b2 (Divide -20 by 5, subtract a exponents, subtract b exponents)

500

Arrange from least to greatest:

2\sqrt{9}, \sqrt{40}, 6.1.


    • Answer: 

      2\sqrt{9}, 6.1, \sqrt{40}.

      • Why?

      • 2\sqrt{9} = 2(3) = 6

      • 6.1 = 6.1

      • \sqrt{40} \approx 6.3 sqrt 36 = 6)

        .