Basic Math Examples

$(\frac{\sqrt{144}}{14 - 8} + 5^{2}) + {(\sqrt{64} - \sqrt{1})}^{2}$

Step 1

Find the common denominator.

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Step 1.1

Subtract $8$ from $14$ .

$\frac{\sqrt{144}}{6} + 5^{2} + {(\sqrt{64} - \sqrt{1})}^{2}$

Step 1.2

Write $5^{2}$ as a fraction with denominator $1$ .

$\frac{\sqrt{144}}{6} + \frac{5^{2}}{1} + {(\sqrt{64} - \sqrt{1})}^{2}$

Step 1.3

Multiply $\frac{5^{2}}{1}$ by $\frac{6}{6}$ .

$\frac{\sqrt{144}}{6} + \frac{5^{2}}{1} \cdot \frac{6}{6} + {(\sqrt{64} - \sqrt{1})}^{2}$

Step 1.4

Multiply $\frac{5^{2}}{1}$ by $\frac{6}{6}$ .

$\frac{\sqrt{144}}{6} + \frac{5^{2} \cdot 6}{6} + {(\sqrt{64} - \sqrt{1})}^{2}$

Step 1.5

Write ${(\sqrt{64} - \sqrt{1})}^{2}$ as a fraction with denominator $1$ .

$\frac{\sqrt{144}}{6} + \frac{5^{2} \cdot 6}{6} + \frac{{(\sqrt{64} - \sqrt{1})}^{2}}{1}$

Step 1.6

Multiply $\frac{{(\sqrt{64} - \sqrt{1})}^{2}}{1}$ by $\frac{6}{6}$ .

$\frac{\sqrt{144}}{6} + \frac{5^{2} \cdot 6}{6} + \frac{{(\sqrt{64} - \sqrt{1})}^{2}}{1} \cdot \frac{6}{6}$

Step 1.7

Multiply $\frac{{(\sqrt{64} - \sqrt{1})}^{2}}{1}$ by $\frac{6}{6}$ .

$\frac{\sqrt{144}}{6} + \frac{5^{2} \cdot 6}{6} + \frac{{(\sqrt{64} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{\sqrt{144} + 5^{2} \cdot 6 + {(\sqrt{64} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3

Simplify each term.

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Step 3.1

Rewrite $144$ as $12^{2}$ .

$\frac{\sqrt{12^{2}} + 5^{2} \cdot 6 + {(\sqrt{64} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3.2

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

$\frac{12 + 5^{2} \cdot 6 + {(\sqrt{64} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3.3

Raise $5$ to the power of $2$ .

$\frac{12 + 25 \cdot 6 + {(\sqrt{64} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3.4

Multiply $25$ by $6$ .

$\frac{12 + 150 + {(\sqrt{64} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3.5

Simplify each term.

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Step 3.5.1

Rewrite $64$ as $8^{2}$ .

$\frac{12 + 150 + {(\sqrt{8^{2}} - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3.5.2

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

$\frac{12 + 150 + {(8 - \sqrt{1})}^{2} \cdot 6}{6}$

Step 3.5.3

Any root of $1$ is $1$ .

$\frac{12 + 150 + {(8 - 1 \cdot 1)}^{2} \cdot 6}{6}$

Step 3.5.4

Multiply $- 1$ by $1$ .

$\frac{12 + 150 + {(8 - 1)}^{2} \cdot 6}{6}$

Step 3.6

Subtract $1$ from $8$ .

$\frac{12 + 150 + 7^{2} \cdot 6}{6}$

Step 3.7

Raise $7$ to the power of $2$ .

$\frac{12 + 150 + 49 \cdot 6}{6}$

Step 3.8

Multiply $49$ by $6$ .

$\frac{12 + 150 + 294}{6}$

Step 4

Simplify the expression.

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Step 4.1

Add $12$ and $150$ .

$\frac{162 + 294}{6}$

Step 4.2

Add $162$ and $294$ .

$\frac{456}{6}$

Step 4.3

Divide $456$ by $6$ .

$76$