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1.

Choose all that apply:

Rational Numbers are...

numbers that can be written as a fraction

numbers that have repeating decimals

numbers that have decimals that never end and do not repeat

numbers that cannot be negative

numbers that are have a decimal that does not continue on forever
2.
Choose all that apply:

Irrational Numbers are...

numbers that have decimals that do not repeat

numbers that have decimals that do not stop

numbers that can be written as a fraction

numbers that can only be negative
3.
Choose all below that are irrational numbers.

4.567647...

4.
What is
as a decimal?





none of these
5.
Convert
to a fraction.

6.
Given a square with an area of 64, what is the length of each side.

8

16

32

64
7.
In the expression
the symbol over the x is called a:

radical

radicand

cubed root
8.
Choose all that apply below:

5 is equivalent to...

9.
An example of a perfect square number is:

9

10

11

12
10.
An example of a perfect cubed number is:

27

28

30

35
11.
Which are examples of Pythagorean Triples?

3,4,5

7,24,25

5,12,14

20,21,30
12.
Given that the two legs of a right triangle are 8 and 15, what is the length of the hypotenuse?

17

23

7

289
13.
Is the triangle shown below a right triangle?

Yes, because 5,12,13 is a Pythagorean Triple.

No, 5,12,13 is not a Pythagorean Triple.

There is not enough information to decide

1 answer

Certainly! Here are the answers and explanations for each of the questions:

  1. Rational Numbers are...

    • numbers that can be written as a fraction (True)
    • numbers that have repeating decimals (True)
    • numbers that have decimals that never end and do not repeat (False - this describes irrational numbers)
    • numbers that cannot be negative (False - rational numbers can be negative)
    • numbers that have a decimal that does not continue on forever (True - this applies to rational numbers)

  2. Irrational Numbers are...

    • numbers that have decimals that do not repeat (True)
    • numbers that have decimals that do not stop (True)
    • numbers that can be written as a fraction (False - this describes rational numbers)
    • numbers that can only be negative (False - irrational numbers can be both positive and negative)

  3. Choose all that are irrational numbers:

    • 4.567647... (This number has a non-repeating and non-terminating decimal, therefore it is an irrational number)

  4. What is √2 as a decimal?

    • The decimal is approximately 1.414 (often rounded to a few significant figures). If "none of these" is an option, it would depend on the provided choices.

  5. Convert 0.75 to a fraction:

    • 0.75 can be converted to the fraction 3/4.

  6. Given a square with an area of 64, what is the length of each side?

    • The length of each side is 8 (because √64 = 8).

  7. In the expression √x the symbol over the x is called a:

    • radical (The entire symbol √ is called a radical, while x is the radicand.)

  8. Choose all that apply below: 5 is equivalent to...

    • Since options aren’t provided, generally, 5 can be equivalent to 5/1, or 5.0, etc. It depends on the options.

  9. An example of a perfect square number is:

    • 9 (because it is 3²).

  10. An example of a perfect cubic number is:

    • 27 (because it is 3³).

  11. Which are examples of Pythagorean Triples?

    • 3,4,5 (True, since \(3^2 + 4^2 = 5^2\))
    • 7,24,25 (True, since \(7^2 + 24^2 = 25^2\))
    • 5,12,14 (False, since \(5^2 + 12^2 ≠ 14^2\))
    • 20,21,30 (False, since \(20^2 + 21^2 ≠ 30^2\))

  12. Given that the two legs of a right triangle are 8 and 15, what is the length of the hypotenuse?

    • Using the Pythagorean theorem: hypotenuse = √(8² + 15²) = √(64 + 225) = √289 = 17.

  13. Is the triangle shown below a right triangle?

    • If the sides are 5, 12, and 13, then:
      • Yes, because 5, 12, 13 is a Pythagorean Triple.

If you have specific numbers or choices for some questions, feel free to share, and I can help refine the answers!