Question

Prove that 7-2√3 is irrational number​

Answer 1

Answer: by using contradiction method

Step-by-step explanation: consider that 7-2√3 is rational so their must be a fractional form of itna/b

Answer 2

Step-by-step explanation:

Let assume that 7-2root3 be rational and rational numbers are in the form of p/q form.

7 - 2 \sqrt{3} = \frac{p}{q} \\

7 - \frac{p}{q} = 2\sqrt{3} \\

\frac{7q - p}{q} = 2\sqrt{3} \\

\frac{7q - p}{2q} = \sqrt{3} \\

We know that root 3 is irrational and not p/q form. It contradicts the statement that it is irrational as it is p/q form.

Subtraction and multiplication of irrational number form irrational number so

7-2root3 is irrational.