Simplify cube root of 8x^7y^9z^3

Problem

√(3,8*x7*y9*z3)

Solution

1. Rewrite the expression by factoring the terms inside the radical into perfect cubes.

√(3,2⋅x6⋅x⋅y9⋅z3)

2. Apply the product property of radicals to separate the perfect cubes from the remaining factors.

√(3,2)⋅√(3,x6)⋅√(3,y9)⋅√(3,z3)⋅√(3,x)

3. Evaluate the cube roots of the perfect cubes by dividing their exponents by 3.

2⋅x2⋅y3⋅z⋅√(3,x)

4. Combine the terms outside the radical to reach the final simplified form.

2*x2*y3*z√(3,x)

Final Answer

√(3,8*x7*y9*z3)=2*x2*y3*z√(3,x)

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