**Square Root ((Reference))**

The square root of a positive number

Every positive number has two square roots, one positive and one negative. They are opposites of each other.

**Principal Square Root **
x
x
((Reference))

If *principal square root* of the number.

**Secondary Square Root **
−
x
−
x
((Reference))

*secondary square root* of the number.

**Radical Sign, Radicand; and Radical ((Reference))**

In the expression

√ is called the *radical sign*.

*radicand*.

*radical*.

The horizontal bar that appears attached to the radical sign, √, is a grouping symbol that specifies the radicand.

**Meaningful Expressions ((Reference))**

A radical expression will only be meaningful if the radicand (the expression under the radical sign) is *not* negative:

**Simplifying Square Root Expressions ((Reference))**

If

**Perfect Squares ((Reference))**

Real numbers that are squares of rational numbers are called *perfect squares*.

**Irrational Numbers ((Reference))**

Any indicated square root whose radicand is not a perfect square is an irrational number.

**The Product Property ((Reference))**

**The Quotient Property ((Reference))**

**Be Careful ((Reference))**

**Simplified Form ((Reference))**

A square root that does not involve fractions is in simplified form if there are no perfect squares in the radicand.

A square root involving a fraction is in simplified form if there are no

- perfect squares in the radicand,
- fractions in the radicand, or
- square root expressions in the denominator

**Rationalizing the Denominator ((Reference))**

The process of eliminating radicals from the denominator is called *rationalizing the denominator*.

**Multiplying Square Root Expressions ((Reference))**

The product of the square roots is the square root of the product.

- Simplify each square root, if necessary.
- Perform the multiplication.
- Simplify, if necessary.

**Dividing Square Root Expressions ((Reference))**

The quotient of the square roots is the square root of the quotient.

**Addition and Subtraction of Square Root Expressions ((Reference))**

**Square Root Equation ((Reference))**

A *square root equation* is an equation that contains a variable under a square root radical sign.

**Solving Square Root Equations ((Reference))**

- Isolate a radical.
- Square both sides of the equation.
- Simplify by combining like terms.
- Repeat step 1 if radical are still present.
- Obtain potential solution by solving the resulting non-square root equation.
- Check potential solutions by substitution.

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