Basic Math Examples

k^{2} = 450

$k^{2} = 450$

Step 1

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

k = \pm \sqrt{450}

$k = \pm \sqrt{450}$

Step 2

Simplify

\pm \sqrt{450}

$\pm \sqrt{450}$ .

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Step 2.1

Rewrite

450

$450$ as

15^{2} \cdot 2

$15^{2} \cdot 2$ .

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Step 2.1.1

Factor

225

$225$ out of

450

$450$ .

k = \pm \sqrt{225 (2)}

$k = \pm \sqrt{225 (2)}$

Step 2.1.2

Rewrite

225

$225$ as

15^{2}

$15^{2}$ .

k = \pm \sqrt{15^{2} \cdot 2}

$k = \pm \sqrt{15^{2} \cdot 2}$

k = \pm \sqrt{15^{2} \cdot 2}

$k = \pm \sqrt{15^{2} \cdot 2}$

Step 2.2

Pull terms out from under the radical.

k = \pm 15 \sqrt{2}

$k = \pm 15 \sqrt{2}$

k = \pm 15 \sqrt{2}

$k = \pm 15 \sqrt{2}$

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.

k = 15 \sqrt{2}

$k = 15 \sqrt{2}$

Step 3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

k = - 15 \sqrt{2}

$k = - 15 \sqrt{2}$

Step 3.3

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

k = 15 \sqrt{2}, - 15 \sqrt{2}

$k = 15 \sqrt{2}, - 15 \sqrt{2}$

k = 15 \sqrt{2}, - 15 \sqrt{2}

$k = 15 \sqrt{2}, - 15 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

k = 15 \sqrt{2}, - 15 \sqrt{2}

$k = 15 \sqrt{2}, - 15 \sqrt{2}$

Decimal Form:

k = 21.21320343 \dots, - 21.21320343 \dots

$k = 21.21320343 \dots, - 21.21320343 \dots$