The value of $\sqrt{1+1}$ is.......

Prove that $\sqrt{2}$ is irrational.

If $HCF(a, b) = 8$,$LCM(a, b) = 64$ and $a > b$,then $a = \dots$

The Least Common Multiple $(LCM)$ of the smallest prime number and the smallest composite number is . . . . . . .

If $\alpha$ and $\beta$ are the zeros of the polynomial $P(x) = x^2 - 3x + 2k$ and $\alpha + \beta = \alpha\beta$,then the value of $k$ is:

If $HCF(a, b) = 12$,then which of the following cannot be the $LCM(a, b)$? Options: $(A) 90, (B) 24, (C) 48, (D) 60$.