Evaluate cube root of 750

Problem

√(3,750)

Solution

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

750=2⋅3⋅5⋅5⋅5

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

750=(5⋅5⋅5)⋅(2⋅3)

750=5⋅6

3. Apply the product property of radicals to separate the perfect cube.

√(3,750)=√(3,5⋅6)

√(3,750)=√(3,5)⋅√(3,6)

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

√(3,5)=5

√(3,750)=5√(3,6)

Final Answer

√(3,750)=5√(3,6)

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