Finite Math Examples

$t^{2} = \frac{153}{16}$

Step 1

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

$t = \pm \sqrt{\frac{153}{16}}$

Step 2

Simplify $\pm \sqrt{\frac{153}{16}}$ .

Tap for more steps...

Step 2.1

Rewrite $\sqrt{\frac{153}{16}}$ as $\frac{\sqrt{153}}{\sqrt{16}}$ .

$t = \pm \frac{\sqrt{153}}{\sqrt{16}}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Rewrite $153$ as $3^{2} \cdot 17$ .

Tap for more steps...

Step 2.2.1.1

Factor $9$ out of $153$ .

$t = \pm \frac{\sqrt{9 (17)}}{\sqrt{16}}$

Step 2.2.1.2

Rewrite $9$ as $3^{2}$ .

$t = \pm \frac{\sqrt{3^{2} \cdot 17}}{\sqrt{16}}$

Step 2.2.2

Pull terms out from under the radical.

$t = \pm \frac{3 \sqrt{17}}{\sqrt{16}}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

Rewrite $16$ as $4^{2}$ .

$t = \pm \frac{3 \sqrt{17}}{\sqrt{4^{2}}}$

Step 2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$t = \pm \frac{3 \sqrt{17}}{4}$

Step 3

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

Tap for more steps...

Step 3.1

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

$t = \frac{3 \sqrt{17}}{4}$

Step 3.2

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

$t = - \frac{3 \sqrt{17}}{4}$

Step 3.3

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

$t = \frac{3 \sqrt{17}}{4}, - \frac{3 \sqrt{17}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{3 \sqrt{17}}{4}, - \frac{3 \sqrt{17}}{4}$

Decimal Form:

$t = 3.09232921 \dots, - 3.09232921 \dots$