Question

prove that root 3 is irrational

Answer 1

Heya Dear !!
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Here Is Your Ans.----->

Let us assume that √3 is a rational number.
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That is, we can find integersaandb(≠ 0) such that √3 = (a/b)

Suppose a and b have a common factor other than 1, then we can divide by the common factor, and assume that a and bare coprime.

√3b = a⇒ 3b2=a2(Squaring on both sides) → (1)Therefore, a2is divisible by 3Hence ‘a’ is also divisible by 3.

So, we can write a = 3c for some integerc.Equation (1) becomes,3b2=(3c)2⇒ 3b2= 9c2∴ b2= 3c2

This means that b2is divisible by 3, and so b is also divisible by 3.Therefore, a and b have at least 3 as a common factor.

But this contradicts the fact that a andb are coprime.

This contradiction has arisen because ofour incorrect assumption that √3 is rational.

So, we conclude that √3 is irrational.

Hence proved <=========

Hope It Helps ☺

Answer 2

Answer:

177Step-by-step explanation: