Cut a square into 6 pieces and form three identical squares from them.

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We will solve the inverse problem: cut three squares with side $a$ and combine them into a square with side $\sqrt{3} a$. The required cuts are shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_55a07599adfd5314dc75g-14.jpg?height=1163&width=1098&top_left_y=339&top_left_x=480)

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