Basic Math Examples

b^{2} = 112

$b^{2} = 112$

Step 1

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

b = \pm \sqrt{112}

$b = \pm \sqrt{112}$

Step 2

Simplify

\pm \sqrt{112}

$\pm \sqrt{112}$ .

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Step 2.1

Rewrite

112

$112$ as

4^{2} \cdot 7

$4^{2} \cdot 7$ .

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Step 2.1.1

Factor

16

$16$ out of

112

$112$ .

b = \pm \sqrt{16 (7)}

$b = \pm \sqrt{16 (7)}$

Step 2.1.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

b = \pm \sqrt{4^{2} \cdot 7}

$b = \pm \sqrt{4^{2} \cdot 7}$

b = \pm \sqrt{4^{2} \cdot 7}

$b = \pm \sqrt{4^{2} \cdot 7}$

Step 2.2

Pull terms out from under the radical.

b = \pm 4 \sqrt{7}

$b = \pm 4 \sqrt{7}$

b = \pm 4 \sqrt{7}

$b = \pm 4 \sqrt{7}$

Step 3

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

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Step 3.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

b = 4 \sqrt{7}

$b = 4 \sqrt{7}$

Step 3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

b = - 4 \sqrt{7}

$b = - 4 \sqrt{7}$

Step 3.3

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

b = 4 \sqrt{7}, - 4 \sqrt{7}

$b = 4 \sqrt{7}, - 4 \sqrt{7}$

b = 4 \sqrt{7}, - 4 \sqrt{7}

$b = 4 \sqrt{7}, - 4 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

b = 4 \sqrt{7}, - 4 \sqrt{7}

$b = 4 \sqrt{7}, - 4 \sqrt{7}$

Decimal Form:

b = 10.58300524 \dots, - 10.58300524 \dots

$b = 10.58300524 \dots, - 10.58300524 \dots$