Undoing a Square

Squaring takes 7 to 49. The square root goes back the other way: it asks which number, squared, gives 49. The answer is 7, written $\sqrt{49} = 7$. The sign √ is the root sign, and the number under it is the one you start from.

Every perfect square has a whole number as its root: $\sqrt{81} = 9$ because ${9}^{2} = 81$, and $\sqrt{25} = 5$. To check a root, square it and see that you land back on the number under the sign. And although -7 squared is also 49, the root sign never gives a negative number, so $\sqrt{49}$ is 7 and only 7.

In a longer line, each root becomes its number first: $\sqrt{81}-\sqrt{25}$ becomes $9-5$, which is 4.