To find the cube root of 343, we are essentially looking for a number that, when multiplied by itself twice (i.e., raised to the power of three), gives 343.
Let's denote this unknown number as [tex]\( x \)[/tex]. Therefore, we have:
[tex]\[ x^3 = 343 \][/tex]
Our goal is to determine the value of [tex]\( x \)[/tex] such that the equation holds true.
To find [tex]\( x \)[/tex], we take the cube root of both sides of the equation:
[tex]\[ x = \sqrt[3]{343} \][/tex]
By computing the cube root of 343, we find that:
[tex]\[ \sqrt[3]{343} \approx 6.999999999999999 \][/tex]
Therefore, the cube root of 343 is approximately:
[tex]\[ \sqrt[3]{343} \approx 6.999999999999999 \][/tex]
Thus, the approximate value of [tex]\( \sqrt[3]{343} \)[/tex] is [tex]\( \boxed{6.999999999999999} \)[/tex].
