Irrational Numbers and Square Roots Quiz

Grade 8 · Math · Quiz

Practice identifying and working with rational and irrational numbers.

Questions

1. Which number is rational?

   1. sqrt(7)
   2. pi
   3. 0.333...
   4. sqrt(3)
   Show answer

   Answer: 0.333...

   0.333... = 1/3 — a repeating decimal that is rational. The others are irrational.

2. The square root of 144 is rational.

   Show answer

   Answer: True

   sqrt(144) = 12 which is a whole number and therefore rational.

3. sqrt(81) = ___.

   Show answer

   Answer: 9

   9 x 9 = 81. So sqrt(81) = 9.

4. Between which integers does sqrt(20) fall?

   1. 3 and 4
   2. 4 and 5
   3. 5 and 6
   4. 2 and 3
   Show answer

   Answer: 4 and 5

   4^2=16 and 5^2=25. Since 16 < 20 < 25, sqrt(20) is between 4 and 5.

5. What is the cube root of 125?

   1. 3
   2. 4
   3. 5
   4. 6
   Show answer

   Answer: 5

   5 x 5 x 5 = 125. So cbrt(125) = 5.

6. Every irrational number is also a real number.

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   Answer: True

   Irrational numbers are a subset of real numbers. Real = rational + irrational.

7. An irrational number's decimal is non-terminating and non-___.

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   Answer: repeating

   Irrational decimals never end (non-terminating) AND have no repeating block.

8. Which is closest to sqrt(10)?

   1. 2.5
   2. 3.0
   3. 3.2
   4. 4.0
   Show answer

   Answer: 3.2

   3.2^2 = 10.24 which is closest to 10. sqrt(10) is approximately 3.162.

9. Which set contains ONLY rational numbers?

   1. {pi, 2, 4}
   2. {1/3, 0.5, 9}
   3. {sqrt(2), 5, 3.14...}
   4. {0.01, sqrt(5), 100}
   Show answer

   Answer: {1/3, 0.5, 9}

   1/3 is a fraction, 0.5=1/2, and 9 is a whole number — all rational.

10. Negative numbers can be perfect squares.

    Show answer

    Answer: False

    You cannot square a real number and get a negative result. Perfect squares are always non-negative.

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