Number Theory

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Pre-Algebra › Number Theory

Questions 1 - 10
1

Which of the following is an irrational number?

Explanation

An irrational number is any number that can not be expressed as a ratio of integers, i.e. a fraction. Therefore, the only irrational number listed is .

2

Which of the following is an irrational number?

Explanation

An irrational number is any number that can not be expressed as a ratio of integers, i.e. a fraction. Therefore, the only irrational number listed is .

3

Which of the following is an irrational number?

Explanation

An irrational number is any number that cannot be written as a fraction of whole numbers. The number pi and square roots of non-perfect squares are examples of irrational numbers.

can be written as the fraction . The term is a whole number. The square root of is , also a rational number. , however, is not a perfect square, and its square root, therefore, is irrational.

4

Which of the following is an irrational number?

Explanation

An irrational number is any number that cannot be written as a fraction of whole numbers. The number pi and square roots of non-perfect squares are examples of irrational numbers.

can be written as the fraction . The term is a whole number. The square root of is , also a rational number. , however, is not a perfect square, and its square root, therefore, is irrational.

5

Which of the following is an integer?

Explanation

The correct answer will yield a whole number as a simplified answer. Integers cannot contain decimals quantities.

The only answer that will yield a whole number term is since simplifying this root will yield .

The correct answer is:

6

Which of the following is an odd number?

I.

II.

III.

IV.

V.

II, III, V

I, III, IV

II, V

I, III, V

II, III, IV

Explanation

Odd numbers are integers that have a ones digit that ends in , , , , or . Choices II, III, V are odd numbers because they have a ones digit of , , and respectively.

7

Which is a square number?

Explanation

Square numbers have one factor. If that factor is multiplied by itself, then the number becomes a perfect square. The only number in the selection that meets this requirement is . We can multiply twice to get the perfect square .

8

Which of the following is an odd number?

I.

II.

III.

IV.

V.

II, III, V

I, III, IV

II, V

I, III, V

II, III, IV

Explanation

Odd numbers are integers that have a ones digit that ends in , , , , or . Choices II, III, V are odd numbers because they have a ones digit of , , and respectively.

9

Which of the following is an integer?

Explanation

The correct answer will yield a whole number as a simplified answer. Integers cannot contain decimals quantities.

The only answer that will yield a whole number term is since simplifying this root will yield .

The correct answer is:

10

Which is a square number?

Explanation

Square numbers have one factor. If that factor is multiplied by itself, then the number becomes a perfect square. The only number in the selection that meets this requirement is . We can multiply twice to get the perfect square .

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