Square Roots
The square root of a number is a number which, when multiplied by itself, gives the original number. For example:
When we take the square root of a number, we use only the non-negative root. Therefore:
However, when we look for numbers whose square is 16, both a positive and a negative number work:
Therefore, the equation
has two solutions:
So it is important to distinguish between taking a square root and solving an equation with a square:
$√16 = 4$, but $x^2 = 16$ has the solutions $x = 4$ and $x = -4$.
The number inside the square root symbol $√$ is called the radicand. For example, in $√64$, 64 is the radicand.
For higher roots, we write the index above the radical sign. For example, in $√^3{64};$, 64 is the radicand and 3 is the index.
