Simplify the square root of 18m^9

3 m4 • sqrt(2m)

Step-by-step explanation:

STEP 1: Factor 18 into its prime factors

          18 = 2 • 32  

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          9 = 32  

Factors which will remain inside the root are :

          2 = 2  

To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          3 = 3  

At the end of this step the partly simplified SQRT looks like this:

        3 • sqrt (2m9)  

STEP 2: Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x8)=x4

    (3.2) sqrt(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x2•sqrt(x)

    (4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

     SQRT(m9) = m4 • SQRT(m)

4+3x is the answer

hope you got it