What does the square root of 2 look like?
Where
√ 2 = 1.4142136
For a square that has sides equal to 1 unit long, the diagonal of the square is equal to the square root of 2. Thus, if a square is 1 inch by 1 inch, the diagonal equals the square root of 2 inches which is approximately equal to 1.4142136 inches long.
By similar triangles, if a square has sides equal to N units long, then the length of the diagonal will be N times the square root of 2 long. For example, a square with sides equal to 5 units long will have a diagonal equal to 5 times the square root of 2 which is approximately equal to 7.0710678 units long.
What does the square root of 3 look like?
Where
√ 3 = 1.7320508
For a cube that has sides equal to 1 unit long, the diagonal of the cube is equal to the square root of 3. Thus, if a cube is 1 inch by 1 inch by 1 inch, the diagonal equals the square root of 3 which is approximately equal to 1.7320508 inches long.
By similar triangles, if a cube has sides equal to N units long, then the length of the diagonal will be N times the square root of 3 long. For example, a cube with sides equal to 7 units long will have a diagonal equal to 7 times the square root of 3 which is approximately 12.1243557 units long.
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