Solved Examples and Worksheet for Finding the Sum of Rational and Irrational Numbers

Q1The simplest form of 43 + 81 is :

A. 7 + 43
B. 43 + 9
C. 6 + 43
D. 43 + 8

Solutions
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Step: 1
43 + 81
Step: 2
= 43 + 9
  [81 = 9]
Correct Answer is :   43 + 9
Q2A girl is 10 years now. Find her age after 10 years ?

A. (7 + 10) years
B. (3 + 10) years
C. (4 + 10) years
D. (10 + 10) years

Solutions
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Step: 1
Present age of a girl = 10 years
Step: 2
∴ The age of the girl after 10 years = (10 + 10) years
Correct Answer is :   (10 + 10) years
Q3A boy jumps 30 cm for his first jump in a high jump competition. His second jump is 29 cm. How high did he jump in total (in cm)?

A. (3 + 29)
B. (30 + 29)
C. (2 + 29)
D. (29 + 30)

Solutions
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Step: 1
The height of the jump in first attempt = 30 cm
Step: 2
The height of the jump in second attempt = 29 cm
Step: 3
∴ The total height of the jump in both the attempts = (30 + 29) cm
Correct Answer is :   (30 + 29)
Q4A person bought two boxes. One box cost $15 and the other cost $23. What was the total bill (in $) ?

A. (15 + 23)
B. (10 + 15)
C. (23 + 15)
D. (11 + 23)

Solutions
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Step: 1
Cost of one box = $15
Step: 2
Cost of other box = $23
Step: 3
∴ The total bill = $(15 + 23)
Correct Answer is :   (15 + 23)
Q5What is the rational part of 37 + 25614 ?

A. 25
B. 37
C. 25614
D. 37

Solutions
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Step: 1
The expression 37 + 25614 can be written as 37 + 4
  [As 4 is the fourth root of 256.]
Step: 2
25614 is the rational part of the given number
Correct Answer is :   25614
Q6Identify the irrational part of 29 + 7.

A. 7
B. 29 + 7
C. 7
D. 29

Solutions
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Step: 1
The irrational part of 29 + 7 is 7
Correct Answer is :   7
Q7Find half of the perimeter of a rectangular track if its length and width are100 m and 701 m respectively?
A. 2(100 + 701) m
B. (200701) m
C. (100 + 701) m
D. (100701) m

Solutions
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Step: 1
Half of the perimeter of a rectangular track = length + width
Step: 2
= 100 + 701
Step: 3
∴ Half of the perimeter of the rectangular track = (100 +701) m
Correct Answer is :   (100 + 701) m
Q8If a = 7 and b = 10, then what is the value of a + b ?
A. 15 + 7
B. 10 + 7
C. 18 + 7
D. 17 + 7

Solutions
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Step: 1
The value of a + b = 7 + 10
  [since a = 7 and b = 10]
Step: 2
= 10 + 7
Correct Answer is :   10 + 7
Q9If a = 6 and b =5 then find the value of a + b?
A. 6 + 5
B. 3 + 6
C. 11 + 5
D. 5 + 6

Solutions
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Step: 1
Given that a = 6 and b =5
Step: 2
The value of a + b = 6 + 5
Correct Answer is :   6 + 5
Q10If c = 17 and d = 64 then which among the following is irrational?

A. c + d
B. c + d
C. c + d
D. 2d + c

Solutions
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Step: 1
The value of c + d = 17 + 64 = 81, which is a rational number.
Step: 2
The value of c + d = 17 + 64 = 17 + 8 = 25, which is a rational number.
Step: 3
The value of 2d + c = 264 + 17 = 2(8) +17 = 16 + 17 = 33, which is a rational number.
Step: 4
The value of c + d = 17 + 64 = 64 + 17, which is an irrational number.
Correct Answer is :   c + d

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