Simplify cube root of -8x^3

Problem

√(3,−8*x3)

Solution

1. Apply the product property of radicals to separate the constant and the variable terms.

√(3,−8*x3)=√(3,−8)⋅√(3,x3)

2. Evaluate the cube root of the constant −8 by finding the number that, when multiplied by itself three times, equals −8

√(3,−8)=−2

3. Evaluate the cube root of the variable term x3 by using the property √(n,an)=a for odd roots.

√(3,x3)=x

4. Multiply the results together to find the simplified expression.

−2⋅x=−2*x

Final Answer

√(3,−8*x3)=−2*x

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