Question

Prove that √2 is an irrational number. Hence, show that 3 - √2 is an irrational
number.​

Answer 1

$\huge \underline \frak \pink {★彡A᭄ɴsᴡᴇʀ彡★}$

Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero. We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.

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A proof that the square root of 2 is irrational.

2 = (2k)2/b2

b2 = 2k2