CBSE Class 10 Maths (Basic) 2025 · Paper 430/1/1 · Question 26(a)

Real Numbers 3 marks Medium

Prove that

3

is an irrational number.

Answer

3

is irrational: assuming

3 = \frac{p}{q}

with

p, q

coprime gives

p^{2} = 3 q^{2}

, so

3

divides

p

; then

q^{2} = 3 k^{2}

, so

3

divides

q

, which contradicts that

p

and

q

are coprime. Hence proved.

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