Worksheet

Is the sum or product rational or irrational?

Grade 9 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

  1. Esme adds 3 + √2 on a calculator. It shows 4.4142135…. Is 3 + √2 rational or irrational?

    • Irrational: the digits never stop or repeat.
    • Rational: it is a whole number plus a little more.
    • Rational: it can be written as 4.41.

  2. Jun works out √9 + 1/4 on paper. It shows 3.25. Is √9 + 1/4 rational or irrational?

    • Irrational: it has a fraction in it.
    • Rational: the digits stop.
    • Irrational: it has a root in it.

  3. Kira finds the distance around a pizza, 2 × π feet (a big pizza for a small table). It shows 6.2831853…. Is 2 × π rational or irrational?

    • Rational: 2 is a whole number.
    • Rational: it can be written as 6.28.
    • Irrational: the digits never stop or repeat.

  4. Luz adds 1/3 + 1/2 and divides on a calculator. It shows 0.8333…. Is 1/3 + 1/2 rational or irrational?

    • Irrational: it is a sum of two fractions.
    • Rational: the digits repeat a pattern.
    • Irrational: the digits never stop.

  5. Milo's robot works out 4 × √5 (and shows every digit it can). It shows 8.9442719…. Is 4 × √5 rational or irrational?

    • Rational: 4 is a whole number.
    • Rational: it can be written as 8.94.
    • Irrational: the digits never stop or repeat.

  6. Pia's padlock tag shows 2/3 + 1/9 worked out as a decimal. It shows 0.7777…. Is 2/3 + 1/9 rational or irrational?

    • Rational: the digits repeat a pattern.
    • Irrational: it is a sum of two fractions.
    • Irrational: the digits never stop.

  7. Ren adds √3 + 5 on a calculator (the screen runs out of room). It shows 6.7320508…. Is √3 + 5 rational or irrational?

    • Irrational: the digits never stop or repeat.
    • Rational: it can be written as 6.73.
    • Rational: it is a whole number plus a little more.

  8. Tala multiplies two irrational numbers, √2 × √18. It equals √(2 × 18), and the strip is shown. What whole number is the product?

  9. In math club, Ari multiplies two irrational numbers, √5 × √45. It equals √(5 × 45), and the strip is shown. What whole number is the product?

  10. Bo's rug is √10 m by √40 m, so its area is √10 × √40 square meters. It equals √(10 × 40), and the strip is shown. What whole number is the product?

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Is the sum or product rational or irrational?

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

  1. Esme adds 3 + √2 on a calculator. It shows 4.4142135…. Is 3 + √2 rational or irrational?

    • Irrational: the digits never stop or repeat.
    • Rational: it is a whole number plus a little more.
    • Rational: it can be written as 4.41.

  2. Jun works out √9 + 1/4 on paper. It shows 3.25. Is √9 + 1/4 rational or irrational?

    • Irrational: it has a fraction in it.
    • Rational: the digits stop.
    • Irrational: it has a root in it.

  3. Kira finds the distance around a pizza, 2 × π feet (a big pizza for a small table). It shows 6.2831853…. Is 2 × π rational or irrational?

    • Rational: 2 is a whole number.
    • Rational: it can be written as 6.28.
    • Irrational: the digits never stop or repeat.

  4. Luz adds 1/3 + 1/2 and divides on a calculator. It shows 0.8333…. Is 1/3 + 1/2 rational or irrational?

    • Irrational: it is a sum of two fractions.
    • Rational: the digits repeat a pattern.
    • Irrational: the digits never stop.

  5. Milo's robot works out 4 × √5 (and shows every digit it can). It shows 8.9442719…. Is 4 × √5 rational or irrational?

    • Rational: 4 is a whole number.
    • Rational: it can be written as 8.94.
    • Irrational: the digits never stop or repeat.

  6. Pia's padlock tag shows 2/3 + 1/9 worked out as a decimal. It shows 0.7777…. Is 2/3 + 1/9 rational or irrational?

    • Rational: the digits repeat a pattern.
    • Irrational: it is a sum of two fractions.
    • Irrational: the digits never stop.

  7. Ren adds √3 + 5 on a calculator (the screen runs out of room). It shows 6.7320508…. Is √3 + 5 rational or irrational?

    • Irrational: the digits never stop or repeat.
    • Rational: it can be written as 6.73.
    • Rational: it is a whole number plus a little more.

  8. Tala multiplies two irrational numbers, √2 × √18. It equals √(2 × 18), and the strip is shown. What whole number is the product?

    6

  9. In math club, Ari multiplies two irrational numbers, √5 × √45. It equals √(5 × 45), and the strip is shown. What whole number is the product?

    15

  10. Bo's rug is √10 m by √40 m, so its area is √10 × √40 square meters. It equals √(10 × 40), and the strip is shown. What whole number is the product?

    20