Evaluate cube root of 40

Problem

√(3,40)

Solution

1. Identify the radicand and look for perfect cube factors. The number 40 can be factored into its prime components.

40=2⋅2⋅2⋅5

2. Group the factors into a perfect cube. Since 2⋅2⋅2=2=8 we can rewrite the expression.

√(3,40)=√(3,8⋅5)

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

√(3,8⋅5)=√(3,8)⋅√(3,5)

4. Simplify the cube root of the perfect cube. Since 2=8 the cube root of 8 is 2

√(3,8)⋅√(3,5)=2√(3,5)

Final Answer

√(3,40)=2√(3,5)

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