Question

Prove that √3 is an irraional number

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Assume to the contrary that √3 is rational.

then

•        √3 is of form p/q
•         p, q are co-prime
•         q≠0

√3=p/q           ⇒     √3 q=p

Squaring on both the sides,

(√3 q)² = p²

3 q² = p²------------------------------------------------------------------------------------------------1

q²=p²/3       ⇒     p/3 = c(c is a constant)

p=3c-----------------------------------------------------------------------------------------------------2

Substitute 2 in 1

3 q² = (3c)²

q²=9c² / 3

q² = 3c²

q²/3 = c²                   ⇒   q/3 = d

But this is contrary to the condition that p,q are co-prime.

∴ our assumption is wrong.

∴√3 is irrational

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