Grade 9 · Math · Algebra 1

9th grade Is the sum or product rational or irrational? worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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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?
- Rational: it can be written as 4.41.
- Rational: it is a whole number plus a little more.
- Irrational: the digits never stop or repeat.
2.
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?
- Irrational: the digits never stop or repeat.
- Rational: it can be written as 6.28.
- Rational: 2 is a whole number.
3.
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.
- Irrational: the digits never stop.
- Rational: the digits repeat a pattern.
4.
Milo's robot works out 4 × √5 (and shows every digit it can). It shows 8.9442719…. Is 4 × √5 rational or irrational?
- Rational: it can be written as 8.94.
- Rational: 4 is a whole number.
- Irrational: the digits never stop or repeat.
5.
In math club, Noah works out √16 × 0.5. It shows 2. Is √16 × 0.5 rational or irrational?
- Irrational: it has a root in it.
- Irrational: it has a decimal in it.
- Rational: the digits stop.
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?
- Irrational: the digits never stop.
- Rational: the digits repeat a pattern.
- Irrational: it is a sum of two fractions.
Tala multiplies two irrational numbers, √2 × √18. It equals √(2 × 18), and the strip is shown. What whole number is the product?
Zee's robot multiplies two irrational numbers, √2 × √8 (and looks surprised). It equals √(2 × 8), and the strip is shown. What whole number is the product?
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?
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?

9th grade Is the sum or product rational or irrational? worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Is the sum or product rational or irrational?. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can say why 3 + √2 is irrational and 0 × √13 is rational.
I can show that two irrational numbers can make a rational one: √2 × √8 = 4.
I can say whether a claim is always, sometimes or never true, with an example.

Standard: N-RN.B.3

Words to know

rational: Can be written as a fraction of whole numbers; its decimal stops or repeats.

irrational: Cannot be written as a fraction; its decimal never stops or repeats.

nonzero: Any number except 0.

sometimes true: True for some examples and false for others.

example: One case that you work out to test a claim.

Common mistakes

Your child decided a number was rational because part of it was, as in 3 + √2.

Your child took a rounded calculator decimal as the exact number.

Your child called a number irrational because it had a root sign, even though the root works out to a whole number.

What to say

Ask: if the digits of √2 never stop, can the digits of 3 + √2 stop?

Ask: does √2 really stop at 1.41, or do its digits keep going?

Ask: what is √9?

Questions parents ask

What is the most common mistake with is the sum or product rational or irrational??

Your child decided a number was rational because part of it was, as in 3 + √2.

How can I help my child with is the sum or product rational or irrational??

Ask: if the digits of √2 never stop, can the digits of 3 + √2 stop?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

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