Square Roots

Square roots are the numbers that have been turned into squares. They are the opposite of exponents.

Square roots are usually found using the radical sign, which is $$\sqrt{}\,$$, though it can be found using the exponent $$n^\frac{1}{2}\,$$.

Perfect Squares
Below is a list of the first ten perfect squares whose answers are whole numbers.
 * $$\sqrt{1}\, = 1$$
 * $$\sqrt{4}\, = 2$$
 * $$\sqrt{9}\, = 3$$
 * $$\sqrt{16}\, = 4$$
 * $$\sqrt{25}\, = 5$$
 * $$\sqrt{36}\, = 6$$
 * $$\sqrt{49}\, = 7$$
 * $$\sqrt{64}\, = 8$$
 * $$\sqrt{81}\, = 9$$
 * $$\sqrt{100}\, = 10$$

Irrational Squares
Some square roots turn out to be irrational numbers.


 * $$\sqrt{2}\, = 1.41421356237309...$$
 * $$\sqrt{3}\, = 1.73205080756887...$$
 * $$\sqrt{5}\, = 2.23606797749979...$$
 * $$\sqrt{6}\, = 2.449489742783178...$$
 * $$\sqrt{7}\, = 2.645751311064591...$$

Imaginary Squares
Some square roots turn out to be imaginary numbers.


 * $$\sqrt{-9}\, = 3i$$
 * $$\sqrt{-5}\, = i\sqrt{5}\,$$

The square roots of negative numbers are always imaginary numbers; they have no real answer. The only way to obtain real answers from negative numbers are with cubic roots.