Chapter SH, Problem 9.15EP

(a)

To determine

To find: The solution of the equation $x^2=16$ .

Answer to Problem 9.15EP

The solutions of the equation $x^2=16$ are 4 and $-4$ .

Explanation of Solution

Given information:

The given equation is $x^2=16$ .

Calculation:

Solve the equation.

  $\begin{array}{c}{x}^2=16\\ x=\sqrt{16}\\ =\pm 4\end{array}$

So, the solutions of the equation $x^2=16$ are 4 and $-4$ .

To check the solution, substitute the values of $x$ in the equation.

Substitute 4 for $x$ in the equation.

  $\begin{array}{c}{4}^2=16\\ 16=16\end{array}$

Substitute $-4$ for $x$ in the equation.

  $\begin{array}{c}{\left(-4\right)}^2=16\\ 16=16\end{array}$

From the above, it is clear that 4 and $-4$ are the solutions of the equation.

Therefore, the solutions of the equation $x^2=16$ are 4 and $-4$ .

(b)

To determine

To find: The solution of the equation $x^2=144$ .

Answer to Problem 9.15EP

The solutions of the equation $x^2=144$ are 12 and $-12$ .

Explanation of Solution

Given information:

The given equation is $x^2=144$ .

Calculation:

Solve the equation.

  $\begin{array}{c}{x}^2=144\\ x=\sqrt{144}\\ =\pm 12\end{array}$

So, the solutions of the equation $x^2=144$ are 12 and $-12$ .

To check the solution, substitute the values of $x$ in the equation.

Substitute 12 for $x$ in the equation.

  $\begin{array}{c}{\left(12\right)}^2=144\\ 144=144\end{array}$

Substitute $-12$ for $x$ in the equation.

  $\begin{array}{c}{\left(-12\right)}^2=144\\ 144=144\end{array}$

From the above, it is clear that 12 and $-12$ are the solutions of the equation.

Therefore, the solutions of the equation $x^2=144$ are 12 and $-12$ .

(c)

To determine

To find: The solution of the equation $x^2=9$ .

Answer to Problem 9.15EP

The solutions of the equation $x^2=9$ are 3 and $-3$ .

Explanation of Solution

Given information:

The given equation is $x^2=9$ .

Calculation:

Solve the equation.

  $\begin{array}{c}{x}^2=9\\ x=\sqrt{9}\\ =\pm 3\end{array}$

So, the solutions of the equation $x^2=9$ are 3 and $-3$ .

To check the solution, substitute the values of $x$ in the equation.

Substitute 3 for $x$ in the equation.

  $\begin{array}{c}{\left(3\right)}^2=9\\ 9=9\end{array}$

Substitute $-3$ for $x$ in the equation.

  $\begin{array}{c}{\left(-3\right)}^2=9\\ 9=9\end{array}$

From the above, it is clear that 3 and $-3$ are the solutions of the equation.

Therefore, the solutions of the equation $x^2=9$ are 3 and $-3$ .