Evaluate cube root of 875

Problem

√(3,875)

Solution

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

2. Factor the number 875 by checking for divisibility. Since it ends in 5 it is divisible by 5

875=5⋅175

3. Continue factoring the result to find more prime factors.

175=5⋅35

35=5⋅7

4. Group the factors to identify the prime factorization.

875=5⋅5⋅5⋅7

875=5⋅7

5. Apply the property of radicals √(3,a⋅b)=√(3,a)⋅√(3,b) to separate the perfect cube.

√(3,875)=√(3,5⋅7)

6. Simplify the radical by taking the cube root of 5

√(3,5)⋅√(3,7)=5√(3,7)

Final Answer

√(3,875)=5√(3,7)

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