Evaluate cube root of 270

Problem

√(3,270)

Solution

1. Prime factorize the number inside the radical to identify perfect cubes.

270=27⋅10

270=3⋅2⋅5

2. Apply the product property of radicals to separate the perfect cube from the remaining factors.

√(3,3⋅2⋅5)=√(3,3)⋅√(3,2⋅5)

3. Simplify the cube root of the perfect cube and multiply the remaining factors under the radical.

√(3,3)=3

2⋅5=10

Final Answer

√(3,270)=3√(3,10)

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