Question

The square root of which number is rational; a) 7 b) 0.003 c) 13 d) 1.96

Answer 1

Answer:

The square root of d) 1.96 is rational.

This is because

√7 = 2.64575131106... (which is irrational)

√0.003 = 0.05477225575... (which is irrational)

√13 = 3.60555127546... (which is irrational)

√1.96 = 1.4 (which is rational)

∴ Option d) 1.96 is the correct answer

Answer 2

Answer:

The answer is - option d)

Step-by-step explanation:

Reasons

a) square root of 7 = $\sqrt{7}$ = 2.6 approx. = it cannot be expressed in p/q form and also has non-terminating non-repeating decimal expansion.

So it is not a rational number i.e. irrational number

b) square root of 0.003 = $\sqrt{0.003}$ =  it cannot be expressed in p/q form and also has non-terminating non-repeating decimal expansion.

So it is not a rational number i.e. irrational number

c) square root of 13 = $\sqrt{13}$ = 3.6 approx. =  it cannot be expressed in p/q form and also has non-terminating non-repeating decimal expansion.

So it is not a rational number i.e. irrational number

d) square root of 1.96 = $\sqrt{1.96}$ = 1.4 = it can be expressed in p/q form and also has terminating decimal expansion [property of rational number].

So it is a rational number