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Rational and Irrational Numbers, and Surds (Year 10)

Free printable NZ Year 10 maths worksheet: classify numbers as rational or irrational, simplify surds, and calculate exactly with roots and multiples of pi.

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Grade 9 · Math worksheet
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Math

Rational and Irrational Numbers, and Surds

Decide whether each number is rational or irrational, write each surd in simplest form, and calculate exactly (no decimal approximations).

  1. 1.
    Is 16\sqrt{16} rational or irrational?
    • a) Rational
    • b) Irrational
  2. 2.
    Is 24\sqrt{24} rational or irrational?
    • a) Rational
    • b) Irrational
  3. 3.
    Is 5\sqrt{5} rational or irrational?
    • a) Rational
    • b) Irrational
  4. 4.
    Is the number pi rational or irrational?
    • a) Rational
    • b) Irrational
  5. 5.
    Is the number 812 rational or irrational?
    • a) Rational
    • b) Irrational
  6. 6.
    Is the number 0.333... (the digit 3 repeating forever) rational or irrational?
    • a) Rational
    • b) Irrational
  7. 7.
    Write 96\sqrt{96} in its simplest surd form.
  8. 8.
    Write 80\sqrt{80} in its simplest surd form.
  9. 9.
    Write 112\sqrt{112} in its simplest surd form.
  10. 10.
    Write 175\sqrt{175} in its simplest surd form.
  11. 11.
    Calculate exactly, without using a decimal approximation: 6 6\sqrt{6} + 5 6\sqrt{6}
  12. 12.
    Calculate exactly, without using a decimal approximation: 7 6\sqrt{6} - 4 6\sqrt{6}
  13. 13.
    Calculate exactly, leaving your answer as a multiple of pi: 3pi + 2pi
  14. 14.
    Calculate exactly, leaving your answer as a multiple of pi: 12pi - 4pi
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