Evaluate cube root of 375

Problem

√(3,375)

Solution

1. Identify the number under the radical and look for its prime factors.

2. Factor the number 375 by dividing by its smallest prime factors.

375=3⋅125

3. Recognize that 125 is a perfect cube.

125=5⋅5⋅5=5

4. Rewrite the original expression using the prime factorization.

√(3,375)=√(3,3⋅5)

5. Apply the property of radicals √(n,a⋅b)=√(n,a)⋅√(n,b) to simplify.

√(3,3⋅5)=√(3,5)⋅√(3,3)

6. Simplify the cube root of the perfect cube.

5⋅√(3,3)

Final Answer

√(3,375)=5√(3,3)

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