Question

which of the following is not a rational number ?
a) 1
b)1.3 bar on top of 3
c)√5
d)√9​

Answer 1

B is not a rational number.

Answer 2

Answer:

The correct answer is option(c)√5

Step-by-step explanation:

Recall the concept:

A rational number is a number that can be expressed in the form $\frac{p}{q}$, where  p and q are integers and q≠0

a) 1

All integers are rational numbers since all the integers can be expressed in the form  $\frac{p}{q}$

1 can be expressed as $\frac{1}{1}$

Hence 1 is a rational number

b) 1.3 bar on top of 3

1.333333

Every recurring non-terminating decimal can be expressed in the form  $\frac{p}{q}$, Hence every non-terminating recurring decimals are rational number

x = 1.3333........-----------(1)

10x = 13.3333.... -----------(2)

(2)-(1) → 10x - x = 13.333.... - 1.3333

9x = 12

x = $\frac{12}{9}$ = $\frac{4}{3}$

Hence 1.333.. is a rational number

c) √5 cannot be expressed in the form  $\frac{p}{q}$, hence √5 is not a rational number

d) √9​ = ±3, an integer.

Since every integer is a rational number.√9 is a rational number

Hence from the options, the number which is not a rational number is √5

The correct answer is option(c)√5

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