50+ Irrational Numbers worksheets for 7th Grade on Quizizz | Free ... - Free Printable

Let's go through each question one by one and solve them with explanations.

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1. Which of the following is a rational number?

Options:
A) 0.565656...
B) π
C) √8
D) √10

Answer: A) 0.565656...

Explanation:
A rational number is any number that can be expressed as a fraction of two integers (p/q), where q ≠ 0. It includes terminating decimals and repeating decimals.

- A) 0.565656... → This is a repeating decimal, so it's rational. For example, it can be written as 56/99.
- B) π → Irrational (non-repeating, non-terminating)
- C) √8 = 2√2 → Irrational (since √2 is irrational)
- D) √10 → Irrational (not a perfect square)

✔ So, A is rational.

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2. Which number is an irrational number?

Options:
A) 2.5
B) 1/2
C) 5.72314...
D) -17

Answer: C) 5.72314...

Explanation:
Irrational numbers cannot be written as fractions and have non-repeating, non-terminating decimals.

- A) 2.5 → Terminating decimal → Rational (25/10 = 5/2)
- B) 1/2 → Fraction → Rational
- C) 5.72314... → The "..." implies it continues without repeating pattern → Likely irrational (if not specified to repeat)
- D) -17 → Integer → Rational

✔ Since only C has no clear repeating or terminating pattern, it’s likely irrational.

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3. Which of the following sets contains all integers?

Options:
A) {2½, -34, √25, 8.5}
B) {-12, √16, -√4, 15}
C) {1/3, -10, 6/2, -9/3}
D) {-2, π, 2.75, 4}

Answer: B) {-12, √16, -√4, 15}

Explanation:
Integers are whole numbers (positive, negative, or zero) with no fractional or decimal parts.

Let’s check each set:

- A) 2½ = 2.5 → Not integer; 8.5 → Not integer → ✘
- B)
- -12 → Integer
- √16 = 4 → Integer
- -√4 = -2 → Integer
- 15 → Integer
→ All are integers ✔
- C)
- 1/3 → Not integer
- 6/2 = 3 → Integer
- -9/3 = -3 → Integer
→ But 1/3 is not → ✘
- D) π → Irrational, not integer; 2.75 → Not integer → ✘

✔ Only B has all integers.

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4. Which number is an irrational number?

Options:
A) 0.333...
B) Square root of 88
C) Square root of 25
D) -15/7

Answer: B) Square root of 88

Explanation:
- A) 0.333... = 1/3 → Repeating decimal → Rational
- B) √88 → Simplify: √(4×22) = 2√22 → √22 is irrational → So √88 is irrational ✔
- C) √25 = 5 → Integer → Rational
- D) -15/7 → Fraction → Rational

✔ So B is irrational.

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5. Which of the following decimals are irrational?

Options:
A) -335.48
B) .2
C) 3.6 repeating
D) .45556567...

Answer: D) .45556567...

Explanation:
Irrational decimals are non-terminating and non-repeating.

- A) -335.48 → Terminates → Rational
- B) .2 → Terminates → Rational
- C) 3.6 repeating → Repeating decimal → Rational (can be written as fraction)
- D) .45556567... → No clear repeating pattern, and seems non-repeating → Likely irrational

✔ So D is irrational.

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6. Irrational numbers...

Options:
A) reduce to π
B) never end and never repeat
C) never end and never reduce
D) must be negative

Answer: B) never end and never repeat

Explanation:
By definition, irrational numbers are real numbers that cannot be expressed as a fraction and have non-terminating, non-repeating decimal expansions.

- A) False – irrational numbers don’t necessarily reduce to π
- B) True – this is the key characteristic
- C) “Never reduce” is vague; “reduce” isn't standard terminology here
- D) False – irrational numbers can be positive or negative (e.g., √2, -π)

✔ Correct answer: B

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7. A fraction is which type of number?

Options:
(Assuming the options are implied — common ones would be: rational, irrational, integer, etc.)

But since options aren't listed in your image, I'll assume the standard choice.

Answer: Rational number

Explanation:
Any number that can be written as a fraction p/q, where p and q are integers and q ≠ 0, is a rational number.

So, a fraction is a rational number.

✔ Answer: Rational number

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Final Answers Summary:

| Q# | Answer |
|----|--------|
| 1 | A |
| 2 | C |
| 3 | B |
| 4 | B |
| 5 | D |
| 6 | B |
| 7 | Rational number |

Let me know if you want the rest of the quiz solved!