Berlin Papyrus 6619/Examples/Problem 1/Modern Proof

Proof
Let $x$ be the length of the side of the smaller square of the two.

We have:

As this is the side of an actual square we are investigating here, we can dispose of the negative square root.

Thus we have:
 * $y = 8$

and so:
 * $x = \dfrac 3 4 \times 8 = 6$