Prove that 2 + √3 is an irrational number, given that √3 is an

Q) Prove that 2 + √3 is an irrational number, given that √3 is an irrational number.

Ans: Let us assume that 2 + √3 is a rational number

Let 2 + √3 = $Prove that 2 + √3 is$ ; q ≠ 0 and p, q are integers

$Prove that 2 + √3 is$ √3 = $Prove that 2 + √3 is$

Since, p and q are integers; Therefore p – 2q is an integer

Therefore, $Prove that 2 + √3 is$ is a rational number

$Prove that 2 + √3 is$ √3 is a rational number

But it contradicts given condition that √3 is an irrational number

Therefore, 2 + √3 is an irrational number

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