Question

Prove that 3+2√7 is irrational​

Answer 1

To prove: 3 + 2√7 is an irrational number.

Proof:

Let us assume that 3 + 2√7 is a rational number.

So it can be written in the form a/b

3 + 2√7= a/b

Here a and b are coprime numbers and b ≠ 0

Solving 3 + 2√7 = a/b we get,

=>2√7= a/b – 3

=>2√7= (a-3b)/b

=>√7 = (a-3b)/2b

This shows (a-3b)/2b is a rational number. But we know that But √7is an irrational number.

so it contradictsour assumption.

Our assumption of 3 + 2√7 is a rational number is incorrect.

3 + 2√7is an irrational number

Answer 2

Answer:

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Step-by-step explanation:

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