Square Root

The root is the inverse operation to the exponentiation. Given two numbers, called the radicand and index, find a third number, which is called the root, such that when elevated to the index, it is equal to the radicand.

Radicals

The index for the square root is 2, although in this case it is omitted.

Square Root

The square root of a number, a, is accurate when a number is found, b, which when elevated to the square is equal to the radicand: b2 = a.

Square Root

Exact square root

An exact square root has the remainder 0.

Radicand = (Exact root)2

Square Roots

Perfect Square

These are the numbers that have exact square roots.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ...

Not exact square root

If a number is not a perfect square, the square root is no exact.

Radicand = (Root)2 + Remainder

Whole Square Root