CLASSIFYING REAL NUMBERS WORKSHEET

Question 1 : 

Write the name that apply to the number given below. 

√5

Question 2 : 

Write the name that apply to the number given below. 

-16.28

Question 3 : 

Write the name that apply to the number given below. 

√81 / 9

Question 4 : 

Write the name that apply to the number given below. 

-9

Question 5 : 

Write the name that apply to the number given below. 

9

Question 6 : 

Write the name that apply to the number given below. 

2√3

Question 7 : 

Write the name that apply to the number given below. 

√25

Question 8 : 

Write the name that apply to the number given below. 

√250

Detailed Answer Key

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, real. 

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, real. 

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, real.   

Question 4 : 

Write the name that apply to the number given below. 

-9

Answer : 

-9 is negative integer, integer, rational, real.

Question 5 : 

Write the name that apply to the number given below. 

9

Answer : 

9 is whole, positive integer, integer, rational, real.

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, real. 

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, real. 

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, real. 

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