Question

A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?

Answer 1

4

Explanation:

Let x be the unknown number.

`\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}`

Solve the found equation for x:

`\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}`

Therefore, the number squared is:

`\implies x^2=2^2=4`