Simplify

Problem

√(3,54*x*y2)/√(3,2*x*y(−1))

Solution

1. Combine the radicals using the quotient property of radicals, √(n,a)/√(n,b)=√(n,a/b)

√(3,(54*x*y2)/(2*x*y(−1)))

2. Simplify the fraction inside the radical by dividing the coefficients and applying the laws of exponents for the variables.

√(3,54/2⋅x/x⋅(y2)/(y(−1)))

3. Divide the constants and subtract the exponents for the variables, noting that x1/x1=1 and y2/y(−1)=y(2−(−1))=y3

√(3,27⋅1⋅y3)

4. Evaluate the cube root of the resulting expression by taking the cube root of each factor.

√(3,27)⋅√(3,y3)

5. Simplify the final terms since 3=27 and the cube root of y3 is y

3*y

Final Answer

√(3,54*x*y2)/√(3,2*x*y(−1))=3*y

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