Evaluate cube root of 320

Problem

√(3,320)

Solution

1. Identify the prime factors of the number 320

320=2⋅160

320=2⋅2⋅80

320=2⋅2⋅2⋅40

320=2⋅2⋅2⋅2⋅20

320=2⋅2⋅2⋅2⋅2⋅10

320=2⋅2⋅2⋅2⋅2⋅2⋅5

320=2⋅5

2. Rewrite the expression using the prime factorization.

√(3,320)=√(3,2⋅5)

3. Apply the property of radicals √(n,a⋅b)=√(n,a)⋅√(n,b) to separate the perfect cube.

√(3,2⋅5)=√(3,2)⋅√(3,5)

4. Simplify the perfect cube by dividing the exponent by the index of the radical.

√(3,2)=2(6/3)

2=4

5. Combine the simplified coefficient with the remaining radical.

4⋅√(3,5)

Final Answer

√(3,320)=4√(3,5)

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