Roots That Are Not Whole

No whole number squares to 5, but $x^{2} = 5$ still has two solutions. They are written with the square root sign: $x = \pm \sqrt{5}$. These are the exact numbers whose square is 5.

The number $\sqrt{5}$ lies between $\sqrt{4} = 2$ and $\sqrt{9} = 3$. It is approximately 2.236. Keep $\sqrt{5}$ when you want an exact answer. Use a decimal only when an approximation is asked for.

For $x^{2} = a$ with a positive number $a$, the solutions are $x = \pm \sqrt{a}$. If $a$ is a perfect square, the solutions are whole numbers. If not, keep the square root sign in the answer, or give a decimal approximation when it is asked for.