Question

prove that it is irrational
$( \sqrt{2} - 3) ^{2}$
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Answer 1

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As we know that a rational number is represented in the form of p/q where p and q is interger.

⟹√2-√3=p/q

here , squaring on both sides

⟹(√2-√3)²=(p/q)²

⟹√4-2*√2*√3+√9=p²/q²

⟹2-2√6+3=p²/q²

⟹1-2√6=p²/q²

⟹-2√6=p²/q²-1

Here, p²/q²-1 is a rational number and -2√6 is a irrational number.

Since, a rational number can't be equal to the irrational number.our assumption is wrong.

➨ Hence, √2 - √3 is a rational no..