Is the sum or product rational or irrational?

Grade 9 Math Worksheet

Circle the best answer.

1. 1.

   Esme writes 5 + √7 on a worksheet. Is 5 + √7 rational or irrational?

   • Irrational: the result can't be written as a fraction.
   • Rational: 5 is rational, and a rational part makes the whole sum rational.
   • Rational: √7 is about 2.65, so the sum is 7.65.
2. 2.

   Jun's robot shows 3√11, which means 3 × √11. Is 3√11 rational or irrational?

   • Irrational: the result can't be written as a fraction.
   • Rational: 3 is a whole number, so the whole product is rational too.
   • Rational: 3√11 is about 9.95.
3. 3.

   In math club, Kira looks at √2 × √32. Is √2 × √32 rational or irrational?

   • Rational: it works out to a fraction or a whole number.
   • Irrational: both factors are irrational.
   • Irrational: it has roots in it, so it cannot be a fraction.
4. 4.

   Luz's padlock tag shows (4 + √6) + (1 − √6) (two roots that might just cancel). Is (4 + √6) + (1 − √6) rational or irrational?

   • Irrational: both numbers are irrational.
   • Irrational: it has a minus sign, which makes the answer irrational.
   • Rational: it works out to a fraction or a whole number.
5. 5.

   Milo's worksheet shows 0 × √13. Is 0 × √13 rational or irrational?

   • Irrational: a rational times an irrational is irrational.
   • Rational: it works out to a fraction or a whole number.
   • Irrational: it has a root in it.
6. 6.

   Noah writes 0 × π on the board (the shortest problem of the day). Is 0 × π rational or irrational?

   • Irrational: π never stops.
   • Irrational: a rational times an irrational is irrational.
   • Rational: it works out to a fraction or a whole number.
7. 7.

   Tala sorts four cards (one card is secretly a whole number). Which one is a rational number?

   • 2 + √3
   • 2√3
   • √3 + √3
   • (2 + √3) − √3
8. 8.

   Zee's robot shows four cards. Which one is a rational number?

   • √5 × √20
   • 5 + √20
   • √5 + √20
   • 5 × √20
9. 9.

   In math club, Ari looks at four cards. Which one is a rational number?

   • √7 + √7
   • 1 × √7
   • 0 × √7
   • 7 + √7
10. 10.

    Bo's padlock has four buttons, and only the rational one opens it. Which one is a rational number?

    • √8 + √2
    • 8 × √2
    • √8 − 2
    • √8 × √2