Simplify cube root of 54x^17

Problem

√(3,54*x^17)

Solution

1. Factor the constant 54 into its prime factors to identify perfect cubes.

54=2⋅27=2⋅3^3

2. Rewrite the variable x^17 as a product of the largest power divisible by 3 and the remaining factor.

x^17=x^15⋅x^2

3. Group the perfect cube terms together inside the radical.

√(3,3^3⋅x^15⋅2⋅x^2)

4. Apply the property of radicals √(3,a⋅b)=√(3,a)⋅√(3,b) to separate the perfect cubes.

√(3,3^3)⋅√(3,x^15)⋅√(3,2*x^2)

5. Simplify the cube roots of the perfect cubes by dividing the exponents by 3

3⋅x^5⋅√(3,2*x^2)

Final Answer

√(3,54*x^17)=3*x^5√(3,2*x^2)

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