Question

question 2

true or false? justify your reasoning. the square of 13 is an irrational number.

true, the square of 13 is 169 and is an irrational number because it can be written as a fraction of two integers whose denominator is not zero.

true, the square of 13 is 169 and is an irrational number because it cannot be written as a fraction of two integers whose denominator is not zero.

false, the square of 13 is 169 and is a rational number because it cannot be written as a fraction of two integers whose denominator is not zero.

false, the square of 13 is 169 and is a rational number because it can be written as a fraction of two integers whose denominator is not zero.

question 3

to which number sets does \\(0.3333333...\\) belong? select all that apply.

Explanation:

Evaluate the square of 13

Using the Rational Numbers and Irrational Numbers knowledge points:

$$ 13^2 = 13 \times 13 = 169 $$

Classify the resulting number

Using the Rational Numbers knowledge point:
The number \(169\) can be written as the fraction \(\frac{169}{1}\), which is a ratio of two integers with a non-zero denominator. Therefore, \(169\) is a rational number, making the statement false.

Match with the correct option for Question 2

The correct option must state that the statement is false because \(169\) is a rational number that can be written as a fraction of two integers with a non-zero denominator. This matches the fourth option.

Analyze the decimal in Question 3

Using the Rational Numbers and Irrational Numbers knowledge points:
The number \(0.3333333\dots\) is a repeating decimal \(0.\bar{3}\), which can be written as the fraction \(\frac{1}{3}\).

Classify the number sets for Question 3

Since \(0.\bar{3} = \frac{1}{3}\), it belongs to:

• Rational Numbers (can be written as a fraction of integers)
• Real Numbers (all rational and irrational numbers)

Answer:

Question 2

• True, the square of 13 is 169 and is an irrational number because it can be written as a fraction of two integers whose denominator is not zero.
• True, the square of 13 is 169 and is an irrational number because it cannot be written as a fraction of two integers whose denominator is not zero.
• False, the square of 13 is 169 and is a rational number because it cannot be written as a fraction of two integers whose denominator is not zero.
• False, the square of 13 is 169 and is a rational number because it can be written as a fraction of two integers whose denominator is not zero. (Correct answer)

Question 3

The number \(0.3333333\dots\) (or \(0.\bar{3}\)) belongs to the following number sets:

• Rational Numbers (since it can be written as \(\frac{1}{3}\))
• Real Numbers (since all rational numbers are real numbers)