MATH SOLVE

1 month ago

Q:
# What is the Cube Root of 2034?

Accepted Solution

A:

Solution: Cube of Root Of 2034 is 12.67
Methods
Step-by-step solution of the cube root of 2034
Let’s do a quick recap on what cube roots are and the different ways we can represent them.
Cube root is the opposite operation of “cubing” a number. For example, when we say that we cubed the number 2, we are asking what the product is after multiplying 2 three times by itself : 2 x 2 x 2, which gives 8 (so the cube of 2 is 8).
However, when a question asks for a cube root, we ask ourselves: what number when multiplied by itself three times produces that number. To use the same example, if we want to find the cube root of 8, we see that we can multiply 2 x 2 x 2, and the cube root of 8 is 2. Two other ways we can represent the cube root of 2034 is:
Exponent form:
2034
1
/
3
{2034}^{1/3}
2034 1/3
Radical form:
2034
3
\sqrt[3]{2034}
3 2034
If the number is small and perfect, you might be able to tell what the cube root is just by looking at the problem, but sometimes when the number is big, it is best to find the prime factorization of 2034 and rewrite 2034 as its prime factorization.
Remember : Be prepared knowing that sometimes, the cube root of a number may not be perfect. A perfect cube root means that the answer is a whole number and not a decimal. However, if your cube root is not perfect, then you would have a decimal answer.
Since we know that the prime factorization of 2034 is 2^1 × 3^2 × 113^1, we can rewrite the cube root of 2034 like so:
2034
3
=
2
1
×
3
2
×
11
3
1
3
\sqrt[3]{2034} = \sqrt[3]{2^1 × 3^2 × 113^1}
3 2034 = 3 2 1 × 3 2 × 11 3 1
Unfortunately, there is no way to get rid of the cube root so that must mean our answer is not a perfect cube root and the only way is to punch it in the calculator to get a decimal answer. Therefore:
2
1
×
3
2
×
11
3
1
3
=
12.67
\sqrt[3]{2^1 × 3^2 × 113^1} = 12.67
3 2 1 × 3 2 × 11 3 1 = 12.67
Therefore, the cube root of 2034 is 12.67 (3 decimal places).
Find the cube root of more numbers!
You know the saying, “practice makes perfect”? Well, it’s definitely true - take a look at some more problems like this one to become a master at finding the cube root of a number
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