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

Let's go through each question one by one and determine whether the given number is rational or irrational, then explain why.

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1. Is the following number rational or irrational? (77/3)

Answer: A) Rational

✔ Explanation:
A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero.
Here, $ \frac{77}{3} $ is already in the form of a fraction of two integers. Even though it's not a whole number, it's still rational.
So, Rational.

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2. Is the following number rational or irrational? (π / 2)

Answer: B) Irrational

✔ Explanation:
$ \pi $ is an irrational number (cannot be written as a fraction of integers).
Dividing an irrational number by a rational number (like 2) results in an irrational number.
So, $ \frac{\pi}{2} $ is irrational.

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3. Is the following number rational or irrational? (π)

Answer: A) Irrational

✔ Explanation:
$ \pi $ is a well-known irrational number — its decimal representation goes on forever without repeating and cannot be expressed as a simple fraction.

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4. Is the following number rational or irrational? 0.333...

Answer: A) Rational

✔ Explanation:
The number $ 0.\overline{3} $ (repeating 3s) is a repeating decimal, which can be expressed as a fraction:
$$
0.\overline{3} = \frac{1}{3}
$$
Since it’s a repeating decimal, it is rational.

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5. Is the following number rational or irrational? -7341.2

Answer: A) Rational

✔ Explanation:
Any terminating decimal (even if negative) is rational.
$-7341.2$ can be written as $-\frac{73412}{10}$, which is a ratio of two integers.
So, it's rational.

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6. Is the following number rational or irrational? √2

Answer: B) Irrational

✔ Explanation:
$ \sqrt{2} $ is a classic example of an irrational number. It cannot be expressed as a fraction, and its decimal goes on forever without repeating.

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7. Once simplified, is this number rational or irrational? 10√2

Answer: A) Irrational

✔ Explanation:
$ 10\sqrt{2} $ is just $ \sqrt{2} $ multiplied by 10. Since $ \sqrt{2} $ is irrational, multiplying it by a rational number (10) keeps it irrational.
So, $ 10\sqrt{2} $ is irrational.

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8. Once simplified, is this number rational or irrational? (√2) * (√2)

Answer: A) Rational

✔ Explanation:
$$
\sqrt{2} \times \sqrt{2} = (\sqrt{2})^2 = 2
$$
And 2 is a rational number (it's an integer).
So, even though both factors are irrational, their product is rational.

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9. Select the ONLY number that is RATIONAL.

Options:
A) $ \sqrt{2} $
B) $ \pi $
C) $ \frac{1}{3} $
D) $ \sqrt{3} $

Answer: C) $ \frac{1}{3} $

✔ Explanation:
- $ \sqrt{2} $ → irrational
- $ \pi $ → irrational
- $ \frac{1}{3} $ → rational (it's a fraction of two integers)
- $ \sqrt{3} $ → irrational

So, the only rational number among them is $ \frac{1}{3} $.

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✔ Final Answers Summary:

| Q | Answer | Explanation |
|---|--------|-------------|
| 1 | A | $ \frac{77}{3} $ is a fraction of integers → Rational |
| 2 | B | $ \frac{\pi}{2} $: π is irrational, so dividing by 2 keeps it irrational |
| 3 | A | π is irrational |
| 4 | A | 0.333... = $ \frac{1}{3} $ → Rational |
| 5 | A | Terminating decimal → Rational |
| 6 | B | $ \sqrt{2} $ is irrational |
| 7 | A | $ 10\sqrt{2} $ is irrational |
| 8 | A | $ \sqrt{2} \times \sqrt{2} = 2 $ → Rational |
| 9 | C | Only $ \frac{1}{3} $ is rational |

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