find the cubic root of 108
A. 3^3√4
B. 4^3√27
3. ^3√4
4. 4^3√3
The cubic root of 108 can be written as 108^(1/3). Simplifying this expression gives:
108^(1/3) = (2^2 * 3^3)^(1/3) = (2^3 * 3^2)^(1/3) = (2^3)^(1/3) * (3^2)^(1/3) = 2 * 3 = 6.
Therefore, the cubic root of 108 is 6. None of the options given in the answer choices match this value.
To find the cubic root of 108, we need to find the value that, when raised to the power of 3, gives us 108.
The correct answer is:
B. 4^3√27
Let's check if this is correct:
(4^3√27)^3 = 4^(3 * 3√27) = 4^9√27 = 4^(9/3) * 3√27 = 4^3 * 3√27 = 64 * 3√27 = 108
So, the cubic root of 108 is indeed 4^3√27.
To find the cubic root of 108, we can use basic mathematical operations. The cubic root of a number is the number that, when multiplied by itself twice, gives the original number.
One way to find the cubic root is by using a calculator or a math software. Simply enter 108 into the calculator or software and find the cubic root function (often denoted as x^3√y or ∛y).
However, if you are looking for the answer without using a calculator or software, we can evaluate the options given:
A. 3^3√4: This option represents 3 to the power of the cubic root of 4. This is not equal to 108.
B. 4^3√27: This option represents 4 to the power of the cubic root of 27. This is also not equal to 108.
C. ^3√4: This option represents the cubic root of 4. This is not equal to 108.
D. 4^3√3: This option represents 4 to the power of the cubic root of 3. This is not equal to 108 either.
Therefore, none of the given options are equal to the cubic root of 108.