To solve for the cube root of 125, we denote this as [tex]\(\sqrt[3]{125}\)[/tex]. The cube root of a number [tex]\(x\)[/tex] is a value that, when raised to the power of 3, gives [tex]\(x\)[/tex]. In other words, we need to find a number [tex]\(y\)[/tex] such that [tex]\(y^3 = 125\)[/tex].
Analyzing the options provided:
- Option A: 5
Let's calculate [tex]\(5^3\)[/tex]:
[tex]\(5^3 = 5 \times 5 \times 5 = 125\)[/tex]
[tex]\(5\)[/tex] raised to the power of 3 equals 125, so 5 is indeed the cube root of 125.
- Option B: [tex]\(\frac{125}{3}\)[/tex]
Let's calculate [tex]\((\frac{125}{3})^3\)[/tex]:
That’s a more complicated fraction, but let's estimate. Since [tex]\(\frac{125}{3} \approx 41.67\)[/tex], we need [tex]\((\frac{125}{3}) \times (\frac{125}{3}) \times (\frac{125}{3})\)[/tex]. Clearly, [tex]\(41.67^3\)[/tex] will be much larger than 125.
- Option C: 11.2
Let's calculate [tex]\(11.2^3\)[/tex]:
[tex]\(11.2 \times 11.2 \times 11.2 \approx 1400\)[/tex]
[tex]\(11.2^3\)[/tex] would be approximately 1400, which is much larger than 125.
- Option D: 25
Let's calculate [tex]\(25^3\)[/tex]:
[tex]\(25^3 = 25 \times 25 \times 25 = 15625\)[/tex]
[tex]\(25^3\)[/tex] equals 15625, which is significantly larger than 125.
Given these calculations, we notice that only Option A (5) gives us the correct value when cubed.
Therefore, the cube root of 125 is:
[tex]\[
\sqrt[3]{125} = 5
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
