Algebra Tutorials!
Friday 3rd of July Home Square Roots and Radical Expressions Solving Radical Equations Simplifying Radical Expressions Irrational Numbers in General and Square Roots in Particular Roots of Polynomials Simplifying Radical Expressions Exponents and Radicals Products and Quotients Involving Radicals Roots of Quadratic Equations Radical Expressions Radicals and Rational Exponents Find Square Roots and Compare Real Numbers Radicals Radicals and Rational Exponents Theorems on the Roots of Polynomial Equations SYNTHETIC DIVISION AND BOUNDS ON ROOTS Simplifying Radical Expressions Exponents and Radicals Properties of Exponents and Square Roots Solving Radical Equations Rational Exponents and Radicals,Rationalizing Denominators Rational Exponents and Radicals,Rationalizing Denominators Quadratic Roots Exponents and Roots Multiplying Radical Expressions Exponents and Radicals Solving Radical Equations Solving Quadratic Equations by Factoring and Extracting Roots Newton's Method for Finding Roots Roots of Quadratic Equations Studio Roots, Radicals, and Root Functions Review division factoring and Root Finding Radicals Simplifying Radical Expressions Multiplying and Simplifying Radical Expressions LIKE RADICALS Multiplication and Division of Radicals Radical Equations BOUNDING ROOTS OF POLYNOMIALS
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Rational Exponents and Radicals Definitions

Defintion 1: If x ≠ 0, then and is undefined

Defintion 2: If x ≠ 0, then for any rational number n
For any positive integer n and m

Defintion 3: If n is odd, then “nth root of a” is such that If n is even and a > 0, then “principal nth root of a” is such that Defintion 4: If is real, then So, for odd n: such that for even n and a > 0: such that So, for odd n: for even n: for any a. is not a real number if n is even and a < 0 a rational number if a is a perfect nth power (e.g. 9 = 32 is a perfect square) an irrational number if a is not a perfect nth power

Defintion 5: If is real, then Defintion 6: If is real, then From now on r and s are any rational numbers, m, n and k are any intergers.

Rules

Rule 1: Rule 2: Rule 3: Rule 4: For Rule 5: For If are real then Rule 6: If all indicated roots are real then

Rule 8: Sumplifying Radicals - Rationalizing denominator (square roots only!) Simplifying Radicals - We will simplify in each step as example.

Step 1: Rewrite the expression with fractional exponents/powers. By Rules 2, 3 and 5

Step 2: Reduce fractional powers  power = 2/3 - already reduced power = 4/3 - already reduced

Step 3: If fractional power > 1, write it as a mixed fraction, follow example steps. power = 2 - not fractional power power = 2/3 < 1 power = Step 4: Put things back in the main problem Step 5: Pull out factors with integer powers Step 6: Rationalize the denomenator of the 2nd factor

Denomenator , we need to make it , so multiply numerator by  [We get by solving for z]

Step 7: Pull out the common denomenator of the fractional power as  Step 8: Switch back to radical notation —– Now it is fully simplified!