Basic Math Examples

$78 + \frac{96}{\sqrt{78}}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{96}{\sqrt{78}}$ by $\frac{\sqrt{78}}{\sqrt{78}}$ .

$78 + \frac{96}{\sqrt{78}} \cdot \frac{\sqrt{78}}{\sqrt{78}}$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{96}{\sqrt{78}}$ by $\frac{\sqrt{78}}{\sqrt{78}}$ .

$78 + \frac{96 \sqrt{78}}{\sqrt{78} \sqrt{78}}$

Step 1.2.2

Raise $\sqrt{78}$ to the power of $1$ .

$78 + \frac{96 \sqrt{78}}{{\sqrt{78}}^{1} \sqrt{78}}$

Step 1.2.3

Raise $\sqrt{78}$ to the power of $1$ .

$78 + \frac{96 \sqrt{78}}{{\sqrt{78}}^{1} {\sqrt{78}}^{1}}$

Step 1.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$78 + \frac{96 \sqrt{78}}{{\sqrt{78}}^{1 + 1}}$

Step 1.2.5

Add $1$ and $1$ .

$78 + \frac{96 \sqrt{78}}{{\sqrt{78}}^{2}}$

Step 1.2.6

Rewrite ${\sqrt{78}}^{2}$ as $78$ .

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Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{78}$ as $78^{\frac{1}{2}}$ .

$78 + \frac{96 \sqrt{78}}{{(78^{\frac{1}{2}})}^{2}}$

Step 1.2.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$78 + \frac{96 \sqrt{78}}{78^{\frac{1}{2} \cdot 2}}$

Step 1.2.6.3

Combine $\frac{1}{2}$ and $2$ .

$78 + \frac{96 \sqrt{78}}{78^{\frac{2}{2}}}$

Step 1.2.6.4

Cancel the common factor of $2$ .

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Step 1.2.6.4.1

Cancel the common factor.

$78 + \frac{96 \sqrt{78}}{78^{\frac{2}{2}}}$

Step 1.2.6.4.2

Rewrite the expression.

$78 + \frac{96 \sqrt{78}}{78^{1}}$

Step 1.2.6.5

Evaluate the exponent.

$78 + \frac{96 \sqrt{78}}{78}$

Step 1.3

Cancel the common factor of $96$ and $78$ .

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Step 1.3.1

Factor $6$ out of $96 \sqrt{78}$ .

$78 + \frac{6 (16 \sqrt{78})}{78}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $6$ out of $78$ .

$78 + \frac{6 (16 \sqrt{78})}{6 (13)}$

Step 1.3.2.2

Cancel the common factor.

$78 + \frac{6 (16 \sqrt{78})}{6 \cdot 13}$

Step 1.3.2.3

Rewrite the expression.

$78 + \frac{16 \sqrt{78}}{13}$

Step 2

To write $78$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$78 \cdot \frac{13}{13} + \frac{16 \sqrt{78}}{13}$

Step 3

Combine $78$ and $\frac{13}{13}$ .

$\frac{78 \cdot 13}{13} + \frac{16 \sqrt{78}}{13}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{78 \cdot 13 + 16 \sqrt{78}}{13}$

Step 4.2

Multiply $78$ by $13$ .

$\frac{1014 + 16 \sqrt{78}}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1014 + 16 \sqrt{78}}{13}$

Decimal Form:

$88.86985952 \dots$