Question

Is the length of the hypotenuse a rational number? Explain.

Answer 1

For a right triangle, using the Pythagorean theorem you can find the hypotenuse measure as follow:

`\begin{gathered} hypotenuse^2=leg1^2+leg2^2 \\ hypotenuse=√(leg1^2+leg2^2) \\ \\ hypotenuse=√(4^2+6^2) \\ hypotenuse=√(16+36) \\ hypotenuse=√(52) \end{gathered}`

Then, the length of the hypotenuse is √52 inches. The radicand is not a perfect square (has not an exact square root). Therefore, the length of the hypotenuse is not a rational number (it can no be the result of the division of two integers)