help me simplify

Question

square root of 3x³y times square root of 6x²y

Answer 1

Just to help you understand the rules for adding/subtracting exponents and for taking quantities out from under the radical:

 

square root of 3x³y times square root of 6x²y

 

  =  SQRT(3x³y) * SQRT(6x²y)

  =  SQRT(18x⁵y²)

  =  SQRT (2*3*3 * x*x*x*x*x * y*y)

  =  SQRT (3*3 * x*x*x*x * y*y)*SQRT(2*x)

  = 3x²y√(2x)

Answer 2

The square root can be rewritten as a fraction power, that we can distribute to everything under.

 

(3x³y)^1/2  * (6x²y)^1/2

 

√18 * x^5/2 * y^2/2        When multiplying square roots we add the exponents of the variable, and then place it over two

                                 since that is the index value.  Then ask how many times 2 goes in evenly.  The whole values of

                                 variables go out front.  The left overs go under the square root.

 

x²y √(18x)               Now we need to see what perfect square goes evenly into 18.   Perfect squares (1, 4, 9, 16 ...)

                               So we split up √18 = √9 * √2

 

Answer:  3x²y √¯(2x)