## Which of the following are real numbers= 6, √7, 54.77, 8.2309517693…, 4003.676767, 37.1298461503…, 0. 562018672507…, √2, 8.39, 90, √5, 8

Question

Which of the following are real numbers— 6, √7, 54.77, 8.2309517693…, 4003.676767, 37.1298461503…, 0. 562018672507…, √2, 8.39, 90, √5, 82, √15​

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3 months 2021-11-06T13:38:41+00:00 2 Answers 0 views 0

1. Given: The numbers 6, √7, 54.77 , 8.2309517693… , 4003.676767 , 37.1298461503… , 0. 562018672507… , √2 , 8.39 , 90 , √5 , 82 , √15

To find: Which of the following are real numbers?

Solution:

• Real numbers: Real numbers can be defined as the union of both the rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals, and fractions come under real numbers.
• So the numbers which are rational are:

6 = 6/1

54.77 = 5477/100

4003.676767 = 4003676767/1000000

4003.676767…………  =  4,00,36,72,764/999999

8.39 = 839/100

90 = 90/1

82 = 82/1

• The numbers which are irrational are:

√7

8.2309517693……

37.1298461503……

0. 562018672507…….

√2

√5

√15

• So all these numbers are real numbers.