To solve the equation [tex]\( w^3 = 1,000 \)[/tex], we need to isolate [tex]\( w \)[/tex]. Here are the steps to do so:
1. Understand the equation: We have [tex]\( w^3 = 1,000 \)[/tex]. This means we need to find a value for [tex]\( w \)[/tex] that, when cubed, equals 1,000.
2. Isolate [tex]\( w \)[/tex]: To find [tex]\( w \)[/tex], we take the cube root of both sides of the equation:
[tex]\[
w = \sqrt[3]{1,000}
\][/tex]
3. Calculate the cube root: The cube root of 1,000 can be expressed as:
[tex]\[
w = 1,000^{1/3}
\][/tex]
4. Determine the value of the cube root: Evaluating [tex]\( 1,000^{1/3} \)[/tex]:
[tex]\[
1,000^{1/3} = 9.999999999999998
\][/tex]
5. Conclusion: Therefore, the value of [tex]\( w \)[/tex] that solves the equation [tex]\( w^3 = 1,000 \)[/tex] is:
[tex]\[
w \approx 9.999999999999998
\][/tex]
