square root of " XY" is a prime number, xy is even, and x > 4y > 0

Qa: Y

Qb: 1

square root of " XY" is a prime number, xy is even, and x > 4y > 0

Qa: Y

Qb: 1

if we’re saying that \sqrt{\text{xy}}=\text{even prime} and the only even prime is \mathbf{2}, thus,

\sqrt{\text{xy}}=2 \\
(\sqrt{\text{xy}})^2 = 2^2 \\
xy = 4\\
y = \frac{4}{x} \text{ or } x = \frac{4}{y} \hspace{10mm} (Eq1)

Now,we’re given that x > 4y > 0 hence, on substituting the value of x from Eq1 because we’re comparing the value of y in question :

\frac{4}{y}>4y>0 \\
4>4y^2>0 \\
1>y^2>0 \text{ (divide by 4)} \\
1>y \text{ (taking square root)}

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Thank you so much for the solution