Simplify square root of 36x^2y^3

Problem

√(,36*x2*y3)

Solution

1. Apply the product property of radicals to separate the expression into the square root of each individual factor.

√(,36⋅x2⋅y3)=√(,36)⋅√(,x2)⋅√(,y3)

2. Evaluate the square root of the constant and the even power of x

√(,36)=6

√(,x2)=|x|

3. Rewrite the odd power of y as a product of the largest even power and the remaining factor.

√(,y3)=√(,y2⋅y)

4. Simplify the radical for the y terms by taking the square root of the even power.

√(,y2⋅y)=|y|√(,y)

5. Combine the results into a single expression, assuming variables represent non-negative values unless otherwise specified.

6⋅x⋅y√(,y)

Final Answer

√(,36*x2*y3)=6*x*y√(,y)

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