Basic Math Examples

$\sqrt{{(120 ft)}^{2} + {(30 ft)}^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $120 ft$ .

$\sqrt{120^{2} {ft}^{2} + {(30 ft)}^{2}}$

Step 1.2

Raise $120$ to the power of $2$ .

$\sqrt{14400 {ft}^{2} + {(30 ft)}^{2}}$

Step 1.3

Apply the product rule to $30 ft$ .

$\sqrt{14400 {ft}^{2} + 30^{2} {ft}^{2}}$

Step 1.4

Raise $30$ to the power of $2$ .

$\sqrt{14400 {ft}^{2} + 900 {ft}^{2}}$

$\sqrt{14400 {ft}^{2} + 900 {ft}^{2}}$

Step 2

Add $14400 {ft}^{2}$ and $900 {ft}^{2}$ .

$\sqrt{15300 {ft}^{2}}$

Step 3

Rewrite $15300 {ft}^{2}$ as ${(30 ft)}^{2} \cdot 17$ .

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Step 3.1

Factor $900$ out of $15300$ .

$\sqrt{900 (17) {ft}^{2}}$

Step 3.2

Rewrite $900$ as $30^{2}$ .

$\sqrt{30^{2} \cdot 17 {ft}^{2}}$

Step 3.3

Move $17$ .

$\sqrt{30^{2} {ft}^{2} \cdot 17}$

Step 3.4

Rewrite $30^{2} {ft}^{2}$ as ${(30 ft)}^{2}$ .

$\sqrt{{(30 ft)}^{2} \cdot 17}$

$\sqrt{{(30 ft)}^{2} \cdot 17}$

Step 4

Pull terms out from under the radical.

$30 ft \sqrt{17}$

Step 5

Reorder factors in $30 ft \sqrt{17}$ .

$30 \sqrt{17} ft$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$