Radicals

Imagine you run a logistics company and need to build a cube-shaped shipping crate with a fixed maximum volume. You know the volume, but you need to find the length of each edge. Since the volume of a cube is the edge length cubed, how can you work backward to find the edge length?

This can be done using radicals, which represent roots of numbers. In general, these are called n-th roots. The n-th root of a number is the value that, when raised to the n-th power, gives that number. We write it using a radical symbol.

The number inside the radical is called the radicand, and the small number written on the radical is called the index. The index tells us which root to find. It is always a positive integer greater than 1.

If you do not see an index, it is 2, which means the square root. An index of 3 means the cube root, and larger indices represent higher roots.

Now, let’s apply this concept to the shipping crate. We know that its volume is the edge length cubed. So, taking the cube root of the known volume gives us the edge length.

So, radicals help you work backward from a known value to find an unknown quantity.