Question

prove the ✓3 - 2 is irraational , given that √3 is irraational​

Answer 1

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Answer 2

Simple answer:

Difference of a irrational number and a rational number is always a irrational number. So,

∴ $\sqrt{3} -2$ is irrational

Hence Proved

Some-what long answer:

Let's assume that $\sqrt{3} -2$ is rational and is in the form of p/q [Where p and q are rational]. Then,

$\sqrt{3} -2 = p/q\\\sqrt{3} = \frac{p-2q}{q}$

Here in LHS is irrational but RHS is rational this contradicts the fact that $\sqrt{3} -2$ is rational.

∴ $\sqrt{3} -2$ is irrational

Hence proved