Printable Worksheets
Online Lessons
Test Maker™
More

Printable & online resources for educators

JOIN FOR FREE

Printable Worksheets
Online Lessons
Test Maker^TM
Worksheet Generator
Printable Games
Plans & Pricing

Blog
Help

JOIN FOR FREE

Browse All Questions
Questions With Images
Advanced Search

Want to see correct answers?
Login or join for free!

Looking for Arithmetic worksheets?
Check out our pre-made Arithmetic worksheets!

Share/Like This Page

Filter By Grade

Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 11

Browse Questions

All Subjects w/ Images (7040)

By ELA/Literacy Standard
By Math Standard

All Subjects (219442)

Arts (4576)
English Language Arts (66481)
English as a Second Language ESL (44785)
Health and Medicine (9411)
Life Skills (2964)
Math (32275)
Physical Education (4157)
Science (55662)
Social Studies (30308)
Study Skills and Strategies (382)
Technology (2637)
Vocational Education (7167)

Rational and Irrational Numbers Questions - All Grades

You can create printable tests and worksheets from these Rational and Irrational Numbers questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

Previous Page 6 of 9 Next

Select All Questions

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$sqrt(11$ ?

3.336
3.317
3.32
3.3166

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$sqrt(1/900$ ?

0.0333
0.100
0.033
0.333

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.1

Choose the number that is rational.

$sqrt(102/26$
$sqrt(9/100$
$sqrt(5)/31$
$6/sqrt(13)$

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.1

Choose the number that is irrational.

$sqrt25$
$sqrt49$
$3/4$
$sqrt(8/7$

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$sqrt(33/2$ ?

4.06
2.87
4.11
4.07

Grade 9 Rational and Irrational Numbers

$pi$ is a real number.

True
False

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Choose the best answer.

$sqrt(72)/5$ is

between 1 and 1.40.
greater than 2.
between 1.41 and 2.
less than 1.

Grade 7 Rational and Irrational Numbers

Which is the greatest number?

$0bar .7$
$7/10$
0.72
$7/8$

Grade 7 Rational and Irrational Numbers CCSS: 7.NS.A.3

$(6/2-8+1/2)-:-4$

$-18$
$-9/8$
$21/20$
$9/8$

Grade 7 Rational and Irrational Numbers

List all classifications for the number 5.

rational, integer, whole number
rational, whole number, natural number
rational, whole number, natural number, integer
whole number, natural number, integer

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$sqrt(36/45$ ?

0.89443
0.89442
0.89444
0.90000

Grade 7 Rational and Irrational Numbers

A rational number is a number that can be expressed as a ratio (fraction) in the form of N/D, where N and D are integers, and D is not equal to 0.

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$sqrt3$ ?

$1.7$
$1.732$
$1.327$
$1.3$

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Andy wants to prove that the sum of a rational number and irrational number is irrational. He does this by the following.

Given

$x$ is a rational number and

$y$ is an irrational number. Assume that

$x+y$ is rational, and let the sum be represented by

$w$ . Since any rational number can be represented as the division of two integers, let

$x=a/b$ and

$w=c/d$ , where

$a,b,c,d$ are all integers. Therefore,

$x+y=w$ can be written as

$a/b + y = c/d$ . By the subtraction rule of equality,

$y = c/d - a/b$ . Rewriting the difference of the two fractions (using the multiplicative identity and distributive property), this becomes

$y = (cb - ad)/(db)$ . Since integers are closed under subtraction and multiplication,

$cb-ad$ is an integer, and so is

$db$ . Therefore, this would make

$y$ a rational number, by definition of rational numbers. But this contradicts our given, that

$y$ is irrational. Therefore,

$x+y$ must be irrational.

Is this proof correct? If not, why?

Yes, this proof is correct. It is called a proof by contradiction.
No, it is not correct. Andy has to use a two-table format for this to be a valid proof.
No, it is not correct. This only proves that $x+y$ is not rational, but that doesn't necessarily mean it is irrational.
No, it is not correct. Andy cannot prove something by contradiction; he must directly prove it.

Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3

Is the following proof correct? If not, why not?

Prove that

$x*y$ is irrational.
Given

$x$ is rational,

$y$ is irrational. Assume that

$x*y$ is rational, and therefore one can let

$x*y = m/n$ , where

$m,n$ are integers. Since

$x$ is rational, it can be represented as the division of two integers. Let

$x=a/b$ , where

$a,b$ are integers. Therefore,

$(a/b)*y=m/n$ . Applying the multiplicative inverse and associative property, this becomes

$y = (m/n) * (b/a) = (m*b)/(n*a)$ . Since integers are closed under multiplication, this value is rational, by definition of rational numbers, implying that

$y$ is rational. But this contradicts the given. Therefore,

$x*y$ is irrational.

Yes, it is correct.
No, it is not correct. It needs to be in a two-column table format.
No, it is not correct. If $x=0$ , then $x*y$ is rational. At the start, one needs to restrict $x$ to being a non-zero rational number.
No, it is not correct. The proof cannot be done by contradiction. It needs to be shown directly that $x*y$ cannot be rational.

Grade 8 Rational and Irrational Numbers

What is the value of pi

$(pi)$ to 2 decimal places? 3.14

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$3/sqrt8$ ?

1.06076
1.06067
1.06166
1.06066

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.1

$sqrt5/4$ is a rational number.

True
False

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$sqrt(99/100$ ?

0.99498
0.99499
0.99500
0.99487

Grade 8 Rational and Irrational Numbers CCSS: 8.NS.A.2

Which of these is the closest approximation for

$1/sqrt3$ ?

0.57740
0.57735
1.57735
0.05774

Previous Page 6 of 9 Next

Privacy Policy
Terms of Use
Test Maker

FREE Printable Worksheets
Common Core ELA Worksheets
Common Core Math Worksheets

Earn Badges x

You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges.