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Math Tutor's Solution: Cube of Root Of 105 is 4.718
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Math Tutor's Step-by-step solution of the cube root of 105
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 105 is:
- Exponent form:
- Radical form:
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 105 and rewrite 105 as its prime factorization.
Reminder from Math Tutor: 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 105 is 3^1 × 5^1 × 7^1, we can rewrite the cube root of 105 like so:
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:
Therefore, the cube root of 105 is 4.718 (3 decimal places).
Math Tutor Suggests: 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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