# CLASSIFYING RATIONAL AND IRRATIONAL NUMBERS WORKSHEET

## About "Classifying rational and irrational numbers worksheet"

Classifying rational and irrational numbers worksheet :

Worksheet on classifying rational and irrational numbers is much useful to the students who would like to practice problems on real numbers.

## Classifying rational and irrational numbers worksheet - Questions

Write all names that apply to each number.

1)  √5

2)  -16.28

3)  √81 / 9

4)  -9

5)  9

6)  2√3

7)  √25

8)  √250

## Classifying rational and irrational numbers worksheet - Answers

Question 1 :

Write the name that apply to the number given below.

√5

Answer :

5 is in square root. It is a whole number, but it is not a perfect square.

So, √5 is irrational.

Question 2 :

Write the name that apply to the number given below.

-16.28

Answer :

–16.28 is a terminating decimal.

So, -16.28 is rational.

Question 3 :

Write the name that apply to the number given below.

√81 / 9

Answer :

Let us do the possible simplification in the given number.

√81 / 9  =  9 / 9

√81 / 9  =  1

So, √81 / 9 is whole, positive integer, integer, rational.

Question 4 :

Write the name that apply to the number given below.

-9

Answer :

-9 is negative integer, integer, rational.

Question 5 :

Write the name that apply to the number given below.

9

Answer :

9 is whole, positive integer, integer, rational.

Question 6 :

Write the name that apply to the number given below.

2√3

Answer :

We have 3 in square root. 3 is a whole number, but it is not a perfect square.

So, √3 is irrational.

We already know the fact, if an irrational number is multiplied by a rational number, the product is irrational.

Hence, 2√3 is irrational.

Question 7 :

Write the name that apply to the number given below.

√25

Answer :

25 is in square root. 25 is a whole number and also it is a perfect square.

So, we have

√25  =  √(5x5)  =  5

Hence, √25 is whole, positive integer, integer, rational.

Question 8 :

Write the name that apply to the number given below.

√250

Answer :

250 is in square root. We are not sure whether 250 is a perfect square or not.

So, let us simplify the given number.

√250  =  √(5x5x5x2)

√250  =  5√(5x2)

√250  =  5√10

We have 10 in square root. 10 is a whole number, but it is not a perfect square.

So, √10 is irrational.

We already know the fact, if an irrational number is multiplied by a rational number, the product is irrational.

Hence, √250 is irrational.

After having gone through the stuff given above, we hope that the students would have understood "Classifying rational and irrational numbers worksheet".

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