**Sets of real numbers worksheet :**

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

Classify each of the numbers given below by naming the set or sets to which it belongs.

1) 37

2) -98

3) **√5**

**4) **-56.12

5) **2√3**

**6) **7/8

7) 102.353535......

8) **√25**

**Question 1 : **

Classify the number given below by naming the set or sets to which it belongs.

37

**Answer : **

Whole, Integer, Rational

37 is a whole number.

All whole numbers are integers. All integers are rational numbers.

**Question 2 : **

Classify the number given below by naming the set or sets to which it belongs.

-98

**Answer : **

Integer, Rational

-98 is an integer.

All integers are rational numbers.

**Question 3 : **

Classify the number given below by naming the set or sets to which it belongs.

**√5**

**Answer : **

Irrational

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

So, √5 is irrational.

**Question 4 : **

Classify the number given below by naming the set or sets to which it belongs.

-56.12

**Answer : **

Rational

-56.12 is a rational number.

It is not a whole number because it is negative. It is not an integer because there are non-zero digits after the decimal point.

**Question 5 : **

Classify the number given below by naming the set or sets to which it belongs.

**2√3**

**Answer : **

Irrational

**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 6 : **

Classify the number given below by naming the set or sets to which it belongs.

7/8

**Answer : **

Rational

7/8 is a rational number.

It is not a whole number, because it is a fraction of a whole number. It is not an integer because it is not a whole number or the opposite of a whole number.

**Question 7 : **

Classify the number given below by naming the set or sets to which it belongs.

102.353535......

**Answer : **

Rational

102.353535........is a rational number.

Since 102.353535...... is a recurring decimal, it can be converted into fraction. And also it is not a whole number or integer, because it is a fraction.

**Question 8 : **

Classify the number given below by naming the set or sets to which it belongs.

**√25**

**Answer : **

Whole, Integer, Rational

**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, integer, rational**

After having gone through the stuff given above, we hope that the students would have understood "Sets of real numbers worksheet".

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