Evaluate cube root of 250

Problem

√(3,250)

Solution

1. Identify the prime factorization of the number inside the radical.

250=2⋅125

250=2⋅5⋅25

250=2⋅5⋅5⋅5

2. Group the factors into sets of three to identify perfect cubes.

250=2⋅5

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

√(3,250)=√(3,5⋅2)

√(3,250)=√(3,5)⋅√(3,2)

4. Simplify the expression by taking the cube root of the perfect cube.

√(3,5)=5

√(3,250)=5√(3,2)

Final Answer

√(3,250)=5√(3,2)

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