We know that for non-negative numbers [math] \sqrt{a^2 \cdot b^2}=\sqrt{a^2} \cdot \sqrt{b^2} =a \cdot b[/math]. Can we apply the same for the sum? In the example below [math]a[/math] and [math]b[/math] are the legs of a right triangle. According to the Pythagorean Theorem the hypotenuse is [math]\sqrt{a^2+b^2}[/math]. Drag to the left the blue point [math]A[/math] to rotate the leg [math]AC[/math] around point [math]C[/math] until the two legs form one segment. Drag to the left the orange point [math]A[/math] to rotate the hypotenuse around point [math]B[/math] until it comes to the base of the triangle. Compare the lengths [math]\sqrt{a^2+b^2}[/math] and [math]\sqrt{a^2} +\sqrt{b^2} =a + b[/math]