Two Proofs of the Irrationality of the Square Root of 2

<p>The Pythagorean theorem states that the square constructed on the hypotenuse of a right triangle (side&nbsp;<em>c</em>&nbsp;of the triangle in the following image) equals the sum of the squares constructed on the legs (sides&nbsp;<em>a</em>&nbsp;and&nbsp;<em>b&nbsp;</em>in the image). From this identity, it follows that&nbsp;<em>c</em>&nbsp;is equal to the square root of&nbsp;<em>a&sup2; +</em>&nbsp;<em>b&sup2;</em>.</p> <p><img alt="" src="https://miro.medium.com/v2/resize:fit:700/1*dYxuhGiie5d0N7vxK4Liow.png" style="height:685px; width:700px" /></p> <p>Given any unit of measurement, if the two legs of a right triangle are both 1 unit long, according to the Pythagorean theorem, the square constructed on the hypotenuse&nbsp;<em>c&nbsp;</em>must be equal to 1&sup2; + 1&sup2;, that is, 2. It follows that&nbsp;<em>c</em>&nbsp;is equal in this case to the&nbsp;<strong>square root of 2</strong>.</p> <p><a href="https://medium.com/not-zero/two-proofs-of-the-irrationality-of-the-square-root-of-2-fca5c38e44c"><strong>Click Here</strong></a></p>
Tags: Square Root