Grade 9 · Math · Algebra 1

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

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Is the sum or product rational or irrational?

Grade 9 Math Worksheet

NameDate

Circle the best answer.

1.
Esme writes 5 + √7 on a worksheet. Is 5 + √7 rational or irrational?
- 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.
- Irrational: the result can't be written as a fraction.
2.
Jun's robot shows 3√11, which means 3 × √11. Is 3√11 rational or irrational?
- Rational: 3√11 is about 9.95.
- Rational: 3 is a whole number, so the whole product is rational too.
- Irrational: the result can't be written as a fraction.
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.
Luz's padlock tag shows (4 + √6) + (1 − √6) (two roots that might just cancel). Is (4 + √6) + (1 − √6) rational or irrational?
- Irrational: it has a minus sign, which makes the answer irrational.
- Irrational: both numbers are irrational.
- Rational: it works out to a fraction or a whole number.
5.
Milo's worksheet shows 0 × √13. Is 0 × √13 rational or irrational?
- Rational: it works out to a fraction or a whole number.
- Irrational: it has a root in it.
- Irrational: a rational times an irrational is irrational.
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.
Pia's robot adds 0.444… + 1/9, where the 4 repeats forever. Is 0.444… + 1/9 rational or irrational?
- Irrational: it mixes a decimal and a fraction.
- Rational: it works out to a fraction or a whole number.
- Irrational: 0.444… never stops.
8.
In math club, Ren multiplies 0.333… × 3, where the 3 repeats forever. Is 0.333… × 3 rational or irrational?
- Rational: it works out to a fraction or a whole number.
- Irrational: 0.333… never stops.
- Irrational: the answer is 0.999… and never stops.
9.
Tala sorts four cards (one card is secretly a whole number). Which one is a rational number?
- 2√3
- (2 + √3) − √3
- 2 + √3
- √3 + √3
10.
Zee's robot shows four cards. Which one is a rational number?
- 5 × √20
- √5 × √20
- 5 + √20
- √5 + √20

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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