Between Two Whole Numbers

Most whole numbers are not perfect squares, so their roots are not whole. You can still say where such a root lies. Take √(50): 50 sits between the perfect squares 49 and 64, so √(50) sits between their roots, 7 and 8.

Why does that work? A bigger number always has a bigger root, so the order is kept. Since 49 < 50 < 64, the roots line up the same way: √(49) < √(50) < √(64), which is 7 < √(50) < 8.

You can even tell which end it is nearer. 50 is just 1 past 49 and 14 short of 64, so √(50) is only a little more than 7. A calculator says about 7.07.