Task 1. All different products of two different factors from the first five prime numbers are formed. Calculate the square root of the product of the square roots of the obtained products.
Solution. Let $a, b, c, d, e$ be five distinct non-negative numbers. All products of two different factors of these numbers are:

$$
a b, a c, a d, a e, b c, b d, b e, c d, c e, d e \text {. }
$$

Their square roots are:

$$
\sqrt{a b}, \sqrt{a c}, \sqrt{a d}, \sqrt{a e}, \sqrt{b c}, \sqrt{b d}, \sqrt{b e}, \sqrt{c d}, \sqrt{c e}, \sqrt{d e}
$$

and the square root of the product of the obtained square roots is:

$$
\begin{aligned}
A & =\sqrt{\sqrt{a b} \sqrt{a c} \sqrt{a d} \sqrt{a e} \sqrt{b c} \sqrt{b d} \sqrt{b e} \sqrt{c d} \sqrt{c e} \sqrt{d e}} \\
& =\sqrt{\sqrt{(a b)(a c)(a d)(a e)(b c)(b d)(b e)(c d)(c e)(d e)}} \\
& =\sqrt[4]{a^{4} b^{4} c^{4} d^{4} e^{4}}=\sqrt[4]{(a b c d e)^{4}}=a b c d e
\end{aligned}
$$

In cases where we have $a=2, b=3, c=5, d=7, e=11$, then

$$
A=2 \cdot 3 \cdot 5 \cdot 7 \cdot 11=2310
$$