Irrational Numbers Quiz

Grade 8 · Math · Quiz

Classify numbers as rational or irrational and estimate the value of irrational square roots.

Questions

1. Which number is rational?

   1. √5
   2. π
   3. √100
   4. √3
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   Answer: √100

   √100 = 10, which is a whole number and can be written as 10/1 — rational. The others are non-perfect squares or π.

2. Which best describes an irrational number?

   1. A number that can be written as a fraction
   2. A number with a terminating decimal
   3. A number with a decimal that goes on forever without repeating
   4. A negative number
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   Answer: A number with a decimal that goes on forever without repeating

   Irrational numbers have infinite, non-repeating decimal expansions and cannot be expressed as p/q.

3. √80 is between which two consecutive integers?

   1. 8 and 9
   2. 9 and 10
   3. 7 and 8
   4. 10 and 11
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   Answer: 8 and 9

   √64 = 8 and √81 = 9. Since 64 < 80 < 81, √80 is between 8 and 9.

4. Which list contains only irrational numbers?

   1. √2, √4, √6
   2. √3, √7, √11
   3. √9, √16, √25
   4. 1/3, 0.5, π
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   Answer: √3, √7, √11

   3, 7, and 11 are not perfect squares, so their square roots are irrational. √4, √9, √16, √25 are all integers.

5. Which is the best estimate of √45?

   1. 5.5
   2. 6.2
   3. 6.7
   4. 7.1
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   Answer: 6.7

   √36 = 6 and √49 = 7. 45 is much closer to 49 than to 36, so √45 ≈ 6.7. (Actual: 6.708…)

6. Which statement is true?

   1. All square roots are irrational
   2. All irrational numbers are square roots
   3. π is rational because it can be approximated
   4. Irrational numbers are real numbers
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   Answer: Irrational numbers are real numbers

   Irrational numbers belong to the set of real numbers. The other statements contain errors (e.g., √4 = 2 is rational).

7. 0.131313… (the 13 repeating forever) is an irrational number.

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   Answer: False

   0.131313… has a repeating pattern (13), which means it is a rational number. It equals 13/99.

8. The set of all rational AND irrational numbers is called the _____ numbers.

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   Answer: real

   The real number system includes all rational numbers (fractions, terminating decimals, etc.) and all irrational numbers.

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