Simplify: root(x^3)/root(x)?

Multiply powers that are in/out of brackets (You'll see what I mean)
Root x --> is the same as --> x^1/2
When dividing powers with the same base, you subtract the powers.


So,

Root ( x^3) = (x^3)^1/2 = x^3/2

(x^3/2)/(x^1/2) ---> subtraction of the powers

x^3/2 - 1/2 giving x^1 or simply x

If you want to know how to simplify this:
√(x³) / √x

First take the square roots by halving the powers:
√(x³) / √x = x^(3/2) / x^(1/2)

Then divide by subtracting the powers:
√(x³) / √x = x^(3/2) / x^(1/2) = x^(3/2 - 1/2) = x^1

Then note that x^1 is just x
√(x³) / √x = x

x^(3/2)
--------
x^(1/2)

x

RULE
----------
When dividing , subtract indices.

sqrt(x^3) / sqrt(x)
= sqrt(x^3 / x)
= sqrt(x^2)
= +or- x

x^m/x^n=x^(m-n)
here,x^3/x=x^2
God bless you.

√(x^3)/√(x)
= √[(x^3)/x]
= √(x^2)
= x

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√ ̅x̅³̅
—— = √ ̅x̅³̅̅/̅x̅            ← √(a} ̸ √{b) = √(a ̸ b)
√ ̅x̅̅


             = √ ̅x̅²̅                       ← √ ̅u̅²̅ = │u│ for all real numbers u

             = │x│                       ← ANSWER

http://en.wikipedia.org/wiki/Square_root
Scroll down to just below the first graph.


                   ANSWER .          .
➊   │x│... For all real numbers x ... i.e. when x can be negative, positive, or 0.
                        Example:    For x = -5,   
                                                    √ ̅(̅-̅5̅)̅² = │-5│ = 5 not -5 ..
                                                    i.e. √ ̅x̅²̅ = │x│ =  -x,   not x, when x is negative

                            OR
 ➋  x ... if x is given as non-negative.
                   e.g. restricted by x ≥ 0 ...
                   Example: For x = 5,   √ ̅(̅̅5̅)̅² = │5│ = 5 = x


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The square root of X^3 is X^1.5.
The square root of X^1 is X^.5.

X^1.5 / X^.5 equals X^(1.5-.5), or simply X.

Square root is the same as taking the contents to the 1/2 power. Sqrt(X^2) equals X.
Multiplication of the same base requires addition of the exponents. X^2 * X^2 equals X^4.
Division of the same base requires subtraction of the exponents. X^2 / X^2 equals X^0 or 1.