Sure, let's go through these questions one by one:
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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, rational numbers have either terminating or repeating decimals)
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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 positive or negative)
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Choose all below that are irrational numbers.
- 4.567647... (True, as it appears to be a non-repeating, non-terminating decimal)
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What is √2 as a decimal?
- Approximately 1.41421356 (not provided in options, thus "none of these" would be correct if that’s the case)
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Convert 0.75 to a fraction.
- It can be converted to 3/4.
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Given a square with an area of 64, what is the length of each side?
- The side length is √64 = 8.
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In the expression √x, the symbol over the x is called a:
- Radical.
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Choose all that apply below: 5 is equivalent to...
- (This question seems incomplete since no options are provided, but the typical equivalences could include 5/1, etc.)
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An example of a perfect square number is:
- 9 (since 3 × 3 = 9)
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An example of a perfect cube number is:
- 27 (since 3 × 3 × 3 = 27)
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Which are examples of Pythagorean Triples?
- 3, 4, 5 (3² + 4² = 5²)
- 7, 24, 25 (7² + 24² = 25²)
- 5, 12, 14 (not a triple, as 5² + 12² ≠ 14²)
- 20, 21, 30 (not a triple, as 20² + 21² ≠ 30²)
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Given that the two legs of a right triangle are 8 and 15, what is the length of the hypotenuse?
- Using the Pythagorean theorem: √(8² + 15²) = √(64 + 225) = √289 = 17.
If you have more questions or need further clarification, feel free to ask!