Question

Which number produces an irrational number when added to 0.5

a. 0.555...
b. square root of 3
c 1/3
d. square root of 16

Answer 1

B) square root of 3



Repeating decimals are rational, surprisingly enough.
Fractions are rational.
The square root of 16 is 4, which is rational.

Answer 2

Answer: Option (b) is the correct answer.

Explanation:

A number which cannot be expressed in the form of
`(p)/(q)` is known as irrational number. An irrational number are non-terminating and non-repeating numbers.

For example, 0.5, square root of 2 etc are irrational numbers.

Sum of a rational number and irrational number always produces an irrational number. Therefore, 0.5 which can also be written as
`(1)/(2)` when added to square root of 3 will produce an irrational number.

Whereas 0.555... is non-terminating and repeating. Hence, it is not an irrational number.

Similarly,
`(1)/(3)` and square root of 16 are rational numbers.

Thus, we can conclude that out of the given options, square root of 3 produces an irrational number when added to 0.5.