Simplify cube root of 54- cube root of 16

Problem

√(3,54)−√(3,16)

Solution

1. Factor the radicands into their prime factors to identify perfect cubes.

√(3,2⋅3⋅3⋅3)−√(3,2⋅2⋅2⋅2)

2. Rewrite the expressions by grouping the perfect cubes.

√(3,3⋅2)−√(3,2⋅2)

3. Simplify the radicals by taking the cube root of the perfect cubes.

3√(3,2)−2√(3,2)

4. Combine the like terms by subtracting the coefficients.

(3−2)√(3,2)

1√(3,2)

Final Answer

√(3,54)−√(3,16)=√(3,2)

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