Question

On a chapter test, Stephanie uses the rules of equation solving and inverse operations to solve the cubic equation below. The directions on the test are not very specific, however, they do say to give an exact solution. Stephanie is not sure if she should submit a decimal approximation or a simplified radical as the answer.

4x3 = 756

What recommendation can you make to Stephanie regarding her answer to the cubic equation above? In your recommendation, explain what the term "exact" indicates with regards to the solution.
Solve the cubic equation from Stephanie’s test. Submit two solutions for the equation- a) your answer as a decimal approximation, rounded to the nearest hundredth, and b) as a simplified radical. Use substitution to check each version of your solution in the original equation.
After solving the test question and checking both the decimal solution and the simplified radical form, would you change your recommendation (in Part 1) to Stephanie regarding the format of her answer? Use complete sentences to explain your reasoning.

Answer 1

Answer:

Step-by-step explanation:

Our aim is to find the best answer to this test question.

Since, we are asked to present an exact solution, we are not able to give approximations.

The term exact means that you need to give the answer like this:

$4x^{3} = 756\\x^{3} = \frac{756}{4} \\x^{3} = 189\\x = \sqrt[3]{189}$

If we were asked to give an approximate result it would be like this x = 5,738.

Hence, our answer is $x = \sqrt[3]{189}$

Answer 2

Answer:

Step-by-step explanation:

look at the one above this