# Radicals and Rational Exponents

**Definition of the Principal Square **

Root

• If a is nonnegative real number, the

nonnegative number b such that

denoted by ,is the **principle square **

root of a

**Square Roots of Perfect Square**

**The Product Rule for Square Roots**

• If a and b represent nonnegative real

number, then

and

• The square root of product is the product

of the square roots

**Text Example **

• Simple :

**solution :**

**The Quotient Rule for Square Roots**

• If a and b does represent nonnegative real

numbers and b does no equal 0, then

and

• The square root of quotient is the

quotient of the square roots

**Text Example**

• Simple :

**solution :**

**Example **

• Perform the indicated operation:

**solution :**

• Perform the indicated operation:

**solution **:

**Definition of the Principal nth Root **

of a Real Number

means that

• If n ,the index , is even , then a is

nonnegative (a≥0)and b is also

nonnegative (b≥0).If n is odd ,a and b

can be any real numbers.

**Finding the nth Roots of Perfect **

th Powers

If n is odd ,

If n is even

**The Product and Quotient Rules **

for nth Roots

• For all real numbers ,where the indicated

roots represent real numbers,

and

** Definition of Rational Exponents**

Furthermore

**Example **

• Simple :

**solution:**

**Definition of Rational Exponents**

•The exponents m/n consists of two parts :the

denominator n is the root and the numerator

m is the exponent. Furthermore .