Evaluate cube root of 10.648

Problem

√(3,10.648)

Solution

1. Convert the decimal to a fraction to make it easier to identify perfect cubes.

√(3,10.648)=√(3,10648/1000)

2. Apply the quotient property of radicals, which states that the root of a fraction is the root of the numerator divided by the root of the denominator.

√(3,10648)/√(3,1000)

3. Evaluate the cube root of the denominator, noting that 10=1000

√(3,1000)=10

4. Factor the numerator to find its cube root. Since 20=8000 and 22=10648 the cube root is 22.

√(3,10648)=22

5. Divide the results to find the final decimal value.

22/10=2.2

Final Answer

√(3,10.648)=2.2

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