Q. 15

Prove that √ 3-√2 is irrational.

Answer :


Let  √3-√2  be a rational number, say r
Then  √3-√2=r
On squaring both sides we have

using (a-b) 2 =a 2 -2ab  +  b 2

Now is a rational number and √6 is an irrational number.
Since a rational number cannot be equal to an irrational number. Our assumption that √
3-√2 is rational is wrong.

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