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Chapter 0: Problem 116

Solve each equation, rounding your answer to four significant digits where necessary. $$ x^{1 / 3}-2=0 $$

Short Answer

Expert verified
We are given the equation \(x^{1/3} - 2 = 0\). To isolate x, we add 2 to both sides: \(x^{1/3} = 2\). Next, we raise both sides to the power of 3: \(x = 8\). Since the result is a whole number, there is no need to round. The final answer is \(x = 8\).

Step by step solution

01

Rewrite the equation to isolate the term containing x

First, add 2 to both sides of the equation to isolate the term containing x: \(x^{1/3} - 2 + 2 = 0 + 2\) So, we get \(x^{1/3} = 2\)
02

Remove the cube root

In order to remove the cube root, we can raise both sides of the equation to the power of 3. This should give us: \((x^{1/3})^3 = 2^3\)
03

Calculate the power

Now, we calculate the power for both sides of the equation: \(x = 8\)
04

Round the result

Since the result is a whole number, we don't need to round the result in this case, and the final answer is: \(x = 8\)

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