To find the cube root of [tex]\(0.125\)[/tex], we denote it as [tex]\(\sqrt[3]{0.125}\)[/tex]. We are essentially looking for a number that, when multiplied by itself three times (cubed), equals [tex]\(0.125\)[/tex].
In other words, we need to solve for [tex]\(x\)[/tex] in the equation:
[tex]\[ x^3 = 0.125 \][/tex]
To begin, let's recall that [tex]\(0.125\)[/tex] can be expressed as a fraction:
[tex]\[ 0.125 = \frac{125}{1000} = \frac{1}{8} \][/tex]
Now, we need to find the cube root of [tex]\(\frac{1}{8}\)[/tex]:
[tex]\[ x = \sqrt[3]{\frac{1}{8}} \][/tex]
We know that:
[tex]\[ \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8} \][/tex]
Thus:
[tex]\[ \sqrt[3]{\frac{1}{8}} = \frac{1}{2} \][/tex]
So, the cube root of [tex]\(\frac{1}{8}\)[/tex] is [tex]\(\frac{1}{2}\)[/tex], which is the same as [tex]\(0.5\)[/tex].
Therefore, the cube root of [tex]\(0.125\)[/tex] is:
[tex]\[ \sqrt[3]{0.125} = 0.5 \][/tex]
