Algebra Tutorials! Monday 19th of March

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:

# Simplifying Square Roots That Contain Variables

Next we will simplify a square-root radical whose radicand contains a variable.

Letâ€™s look at these examples.

If x is a nonnegative real number, then:

 since x Â· x = x2 since (x3)2 = x6 Notice that since (x5)2 = x10 Notice that since (x8)2 = x16 Notice that
In each example, the exponent of the variable in the simplified expression is one-half the exponent of the variable in the radicand.

If the power of x in the radicand is not a multiple of 2, we rewrite the radicand as a product of x1 and an even power of x.

 For example, letâ€™s simplify where x is a nonnegative real number. Write x37 as x36 Â· x1. Write as the product of two radicals. Simplify.
In the remainder of this Topic, we will assume that each variable under a radical represents a nonnegative real number.

Be careful:

If x is negative, then

For example, if x = -3: