Question

Prove that 2 + /7 is irrational number

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• Given a number $2+\sqrt{7}$

To Prove:

• We have to prove that Given number is irrational

Solution:

Let us assume $2+\sqrt{7}$ be a rational number

Hence The number can be written in the form of a/b where a and B are not zero co-prime

$\implies 2 + \sqrt{7} = \dfrac{a}{b}$

$\implies \sqrt{7} = \dfrac{a - 2b}{b}$

We know that $\sqrt{7}$ is an irrational number

∴ A Rational number can never be equal to an irrational number

Hence Our assumption is wrong

∴ $2+\sqrt{7}$ is an irrational number

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NOTE:

• This method of proving irrational number is known as Contradiction method
• In this method first we contradict a fact and later proves that our assumption was wrong