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Products of squares and square roots

The product of two or more square numbers is the square of the product of the original numbers. For example:

\begin{align}3^2×2^2&=3×3×2×2\\\\ &=(3×2)×(3×2)\\\\ &=6×6\\\\ &=6^2\end{align}
\begin{align}8^2×5^2&=8×8×5×5\\\\ &=(8×5)×(8×5)\\\\ &=40×40\\\\ &=40^2\end{align}

The square root of a product is the product of the square roots of the original numbers. For example:

\begin{align}\sqrt{100}&=\sqrt{25×4}\\\\ &=\sqrt{25}×\sqrt{4}\\\\ &=5×2\\\\ &=10\end{align}
\begin{align}\sqrt{484}&=\sqrt{4×121}\\\\ &=\sqrt{4}×\sqrt{121}\\\\ &=2×11\\\\ &=22\end{align}