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 Depdendent Variable

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 Dependent Variable

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# Square Roots

## Definition of Square Root

Before we define the square root of a number, letâ€™s review what we mean by the square of a number.

â€¢ The square of 5 is 52, which is 25.

â€¢ The square of -5 is (-5)2, which is also 25.

Now we will reverse the squaring process and obtain the square roots of a number.

The square root of a number is a number that when multiplied by itself, gives the original number.

The number 25 has two square roots, -5 and -5. Squaring 5 gives 25, squaring -5 also gives 25.

Each positive real number has two square roots, one positive and the other negative.

The positive square root of a number is called the principal square root. The principal square root of 25 is +5.

The radical symbol, , is used to denote the principle square root of a number.

For example,

The negative of the radical symbol, , denotes the negative square root.

For example,

Note:

The number 0 has a single square root, 0.

A negative real number, for example -25, does not have square roots that are real numbers. Thatâ€™s because a real number times itself always gives a nonnegative number.

 52 = +25 (-5)2 = -25

The expression under the radical symbol is called the radicand.

For example, in the expression , the radicand is 49.

A radical is the part of an expression that consists of a radical symbol and a radicand. In this example, the radical is

A radical expression is an expression that contains a radical.

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