Solve for t s=16t^2

$s = 16 t^{2}$

Step 1

Rewrite the equation as $16 t^{2} = s$ .

$16 t^{2} = s$

Step 2

Divide each term in $16 t^{2} = s$ by $16$ and simplify.

Divide each term in $16 t^{2} = s$ by $16$ .

$\frac{16 t^{2}}{16} = \frac{s}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 t^{2}}{16} = \frac{s}{16}$

Divide $t^{2}$ by $1$ .

$t^{2} = \frac{s}{16}$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \pm \sqrt{\frac{s}{16}}$

Step 4

Simplify $\pm \sqrt{\frac{s}{16}}$ .

Rewrite $\frac{s}{16}$ as ${(\frac{1}{4})}^{2} s$ .

Factor the perfect power $1^{2}$ out of $s$ .

$t = \pm \sqrt{\frac{1^{2} s}{16}}$

Factor the perfect power $4^{2}$ out of $16$ .

$t = \pm \sqrt{\frac{1^{2} s}{4^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} s}{4^{2} \cdot 1}$ .

$t = \pm \sqrt{{(\frac{1}{4})}^{2} s}$

Pull terms out from under the radical.

$t = \pm \frac{1}{4} \sqrt{s}$

Combine $\frac{1}{4}$ and $\sqrt{s}$ .

$t = \pm \frac{\sqrt{s}}{4}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$t = \frac{\sqrt{s}}{4}$

Next, use the negative value of the $\pm$ to find the second solution.

$t = - \frac{\sqrt{s}}{4}$

The complete solution is the result of both the positive and negative portions of the solution.

$t = \frac{\sqrt{s}}{4}$

$t = - \frac{\sqrt{s}}{4}$

$t = \frac{\sqrt{s}}{4}$

$t = - \frac{\sqrt{s}}{4}$