When It Is Not Whole

Part of the Triangles section of Coddy's Geometry journey. Lesson 32 of 71.

Most right triangles are not Pythagorean triples. Then the square root does not come out as a whole number. For example, with legs 2 and 3:

$A right triangle with legs 3 and 2 and unknown hypotenuse c$

Legs 2 and 3

c = √(2^2 + 3^2) = √(13)

13 is not a perfect square, so √13 is the exact length. As a decimal, it is about 3.61. Write √13 ≈ 3.61 with the approximation sign, because the rounded decimal is not exactly equal to the root.

A root is finished when the number under it cannot be made smaller. √(13), √(65) and √(2) stay as they are. You can check the answer in the same way as before: √(13) squared is 13, and 4 + 9 = 13. When the number under the root does have a square factor, you can take that factor out of the root. The next lesson shows how.