Question

Prove that 3-√2 is an irrational
Plz urgent friends dont dare to spam u will spame i will delete ur hole qution and answer ​

Answer 1

$\star\:\:\:\bf\large\underline\blue{Question:-}$

• Prove that $3 - \sqrt{2}$ is irrational.

$\star\:\:\:\bf\large\underline\blue{Proof:-}$

Suppose that $3-\sqrt{2}$ is rational, say r.

Then, $3-\sqrt{2}=r\implies \sqrt{2}=3-r$

As r is rational, therefore, $3-r$ is rational which implies that $\sqrt{2}$ is rational.

But this contradicts that $\sqrt{2}$ is irrational.

Hence, our supposition is wrong.

So,

$3 - \sqrt{2}$ is irrational.

Answer 2

Question:-

Prove that 3-√2 is an irrational

Prove that 3-√2 is an irrationalPlz urgent friends dont dare to spam u will spame i will delete ur hole qution and answer

Answer:-

As 3 is a rational number and √2 is an irrational number there difference will be an irrational number.

on the fact that A rational number when subtracted from an irrational number is always an irrational number.