Finite Math Examples

$f (5 \sqrt{2}) = 7 (5 \sqrt{2})$

Step 1

Simplify.

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Step 1.1

Remove parentheses.

$f \cdot 5 \sqrt{2} = 7 \cdot (5 \sqrt{2})$

Step 1.2

Multiply $5$ by $7$ .

$f \cdot 5 \sqrt{2} = 35 \sqrt{2}$

Step 2

Divide each term in $f \cdot (5 \sqrt{2}) = 35 \sqrt{2}$ by $5 \sqrt{2}$ and simplify.

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Step 2.1

Divide each term in $f \cdot (5 \sqrt{2}) = 35 \sqrt{2}$ by $5 \sqrt{2}$ .

$\frac{f \cdot (5 \sqrt{2})}{5 \sqrt{2}} = \frac{35 \sqrt{2}}{5 \sqrt{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{f \cdot (5 \sqrt{2})}{5 \sqrt{2}} = \frac{35 \sqrt{2}}{5 \sqrt{2}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{f \cdot (\sqrt{2})}{\sqrt{2}} = \frac{35 \sqrt{2}}{5 \sqrt{2}}$

Step 2.2.2

Cancel the common factor of $\sqrt{2}$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{f \cdot \sqrt{2}}{\sqrt{2}} = \frac{35 \sqrt{2}}{5 \sqrt{2}}$

Step 2.2.2.2

Divide $f$ by $1$ .

$f = \frac{35 \sqrt{2}}{5 \sqrt{2}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $35$ and $5$ .

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Step 2.3.1.1

Factor $5$ out of $35 \sqrt{2}$ .

$f = \frac{5 (7 \sqrt{2})}{5 \sqrt{2}}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $5$ out of $5 \sqrt{2}$ .

$f = \frac{5 (7 \sqrt{2})}{5 (\sqrt{2})}$

Step 2.3.1.2.2

Cancel the common factor.

$f = \frac{5 (7 \sqrt{2})}{5 \sqrt{2}}$

Step 2.3.1.2.3

Rewrite the expression.

$f = \frac{7 \sqrt{2}}{\sqrt{2}}$

Step 2.3.2

Cancel the common factor of $\sqrt{2}$ .

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Step 2.3.2.1

Cancel the common factor.

$f = \frac{7 \sqrt{2}}{\sqrt{2}}$

Step 2.3.2.2

Divide $7$ by $1$ .

$f = 7$