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​

Answer 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.

Answer:

           So the all given numbers are real numbers.

Answer 2

Step-by-step explanation:

6, √7, 54.77, 8.2309517693…, 4003.676767, 37.1298461503..., 0. 562018672507…, √2, 8.39, 90, √5, 82, √15