Irrational numbers

Identify, compare, or use irrational numbers.

All objectives

Foundation

16 web questions

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  1. Is $\sqrt{4}$ rational or irrational?
  2. Is $\sqrt{9}$ rational or irrational?
  3. Is $\sqrt{2}$ rational or irrational?
  4. Is $\pi$ rational or irrational?
  5. Is $0.5$ rational or irrational?
  6. Is $0.25$ rational or irrational?
  7. Is $\frac{3}{4}$ rational or irrational?
  8. Is $7$ rational or irrational?
  9. Is $\sqrt{16}$ rational or irrational?
  10. Is $\sqrt{5}$ rational or irrational?
  11. Is $2.75$ rational or irrational?
  12. Is $\sqrt{1}$ rational or irrational?
  13. Circle the irrational number: $3,\ \sqrt{3},\ \frac{1}{2}$.
  14. Circle the rational number: $\pi,\ \sqrt{7},\ 0.8$.
  15. Which is closer to $3$: $\sqrt{10}$ or $\sqrt{8}$?
  16. Complete: an irrational number cannot be written exactly as a fraction. True or false?

Proficient

18 web questions

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  1. Classify $\sqrt{25}$ as rational or irrational.
  2. Classify $\sqrt{11}$ as rational or irrational.
  3. Classify $-\sqrt{3}$ as rational or irrational.
  4. Classify $\frac{22}{7}$ as rational or irrational.
  5. Classify $0.333\ldots$ as rational or irrational.
  6. Classify $1.414213\ldots$ as rational or irrational.
  7. Which is irrational: $\sqrt{36}$ or $\sqrt{6}$?
  8. Which is rational: $\pi$ or $\frac{7}{5}$?
  9. $\sqrt{12}$ is between which two whole numbers?
  10. $\sqrt{20}$ is between which two whole numbers?
  11. As written, is $3.14159$ rational or irrational?
  12. True or false: every terminating decimal is rational.
  13. True or false: every square root is irrational.
  14. Complete: $\sqrt{49}=\square$, so it is .
  15. Complete: $\sqrt{15}$ lies between $\square$ and $\square$.
  16. Which is greater: $\sqrt{8}$ or $2.8$?
  17. Which does not belong: $\sqrt{2},\ \pi,\ 0.6,\ \sqrt{7}$?
  18. Why is $\sqrt{10}$ irrational? Give one short reason.

Excellence

18 web questions

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  1. A student says $\sqrt{81}$ is irrational because it has a root sign. Correct? Explain.
  2. A student says $0.272727\ldots$ is irrational because it goes on forever. Correct? Explain.
  3. A student says $\pi=\frac{22}{7}$. Correct? Explain.
  4. Which is greater: $\sqrt{18}$ or $4.3$? Show enough working.
  5. Which is smaller: $\sqrt{50}$ or $7.1$? Explain.
  6. Put in ascending order: $3,\ \sqrt{10},\ \pi,\ \sqrt{11}$.
  7. Put in descending order: $\sqrt{5},\ 2.3,\ \frac{9}{4},\ \sqrt{6}$.
  8. $\sqrt{30}$ lies between which consecutive integers?
  9. $\sqrt{70}$ lies between which consecutive integers?
  10. Complete: an irrational number is a terminating decimal.
  11. Complete: $\sqrt{\square}$ is rational when the number inside is a perfect square.
  12. Which does not belong: $\sqrt{9},\ \sqrt{16},\ \sqrt{18},\ \sqrt{25}$?
  13. Which does not belong: $0.125,\ \frac{1}{8},\ \sqrt{2},\ 2.5$?
  14. Is $2\pi$ rational or irrational? Give a short reason.
  15. Is $\sqrt{3}+1$ rational or irrational? Give a short reason.
  16. A square has area $12 cm^2$. Its side length is $\sqrt{12}$ cm. Between which two whole cm does it lie?
  17. A circle has diameter $1$ m. Is circumference $\pi$ m rational or irrational?
  18. Why is $1.414$ rational even though it approximates an irrational number?