# 4.04: Radicals

- Page ID
- 1103

## Definition of a radical

When people talk of a “square root,” they’re referring to a radical with a root of 2. This is mathematically equivalent to a number raised to the power of 1/2. This equivalence is useful to know when using a calculator to determine a strange root. Suppose for example you needed to find the fourth root of a number, but your calculator lacks a “4th root” button or function. If it has a y^{x} function (which any scientific calculator should have), you can find the fourth root by raising that number to the 1/4 power, or x^{0.25}.

It is important to remember that when solving for an *even* root (square root, fourth root, etc.) of any number, there are *two* valid answers. For example, most people know that the square root of nine is three, but *negative* three is also a valid answer, since (-3)^{2} = 9 just as 3^{2} = 9.