Question

If root 2 is not a rational number then prove that 2 + root 2 is not a rational number

Answer 1

Step-by-step explanation:

let us assume that 2+2√2 is rational.

so So, 2+2√2 = a/b where a and b are integers and co-primes.

2√2 = a/b - 2

2√2 = a-2b /b

 √2 = a-2b /2b

Since product and difference of integers are integers,

a-2b /2b is rational

but we know that √2 is irrational

so this is a contradiction

⇒our assumption is wrong

⇒ 2+2√2 is irrational.

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Answer 2

The step by step solution is given in the above picture

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