Evaluate cube root of 162

Problem

√(3,162)

Solution

1. Find the prime factorization of the number inside the radical to identify perfect cubes.

162=2⋅81

162=2⋅3⋅27

162=2⋅3⋅3⋅3⋅3

162=2⋅3

2. Group the factors into a perfect cube and a remainder.

162=3⋅(2⋅3)

162=27⋅6

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

√(3,27⋅6)=√(3,27)⋅√(3,6)

4. Simplify the cube root of the perfect cube.

√(3,27)=3

Final Answer

√(3,162)=3√(3,6)

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