Evaluate cube root of 500

Problem

√(3,500)

Solution

1. Identify the number under the radical and look for perfect cube factors.

2. Factor the number 500 into a product where one factor is the largest possible perfect cube.

500=125⋅4

3. Apply the product property of radicals, which states that √(3,a⋅b)=√(3,a)⋅√(3,b)

√(3,125⋅4)=√(3,125)⋅√(3,4)

4. Simplify the cube root of the perfect cube. Since 5=125 the cube root of 125 is 5.

√(3,125)=5

5. Combine the simplified coefficient with the remaining radical.

5⋅√(3,4)

Final Answer

√(3,500)=5√(3,4)

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