Finite Math Examples

$4 = \frac{32 k}{\sqrt{4}}$

Step 1

Rewrite the equation as $\frac{32 k}{\sqrt{4}} = 4$ .

$\frac{32 k}{\sqrt{4}} = 4$

Step 2

Multiply both sides of the equation by $\frac{\sqrt{4}}{32}$ .

$\frac{\sqrt{4}}{32} \cdot \frac{32 k}{\sqrt{4}} = \frac{\sqrt{4}}{32} \cdot 4$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{\sqrt{4}}{32} \cdot \frac{32 k}{\sqrt{4}}$ .

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Step 3.1.1.1

Cancel the common factor of $\sqrt{4}$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{\sqrt{4}}{32} \cdot \frac{32 k}{\sqrt{4}} = \frac{\sqrt{4}}{32} \cdot 4$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{32} (32 k) = \frac{\sqrt{4}}{32} \cdot 4$

Step 3.1.1.2

Cancel the common factor of $32$ .

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Step 3.1.1.2.1

Factor $32$ out of $32 k$ .

$\frac{1}{32} (32 (k)) = \frac{\sqrt{4}}{32} \cdot 4$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{32} (32 k) = \frac{\sqrt{4}}{32} \cdot 4$

Step 3.1.1.2.3

Rewrite the expression.

$k = \frac{\sqrt{4}}{32} \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{\sqrt{4}}{32} \cdot 4$ .

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Step 3.2.1.1

Simplify the numerator.

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Step 3.2.1.1.1

Rewrite $4$ as $2^{2}$ .

$k = \frac{\sqrt{2^{2}}}{32} \cdot 4$

Step 3.2.1.1.2

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

$k = \frac{2}{32} \cdot 4$

Step 3.2.1.2

Reduce the expression by cancelling the common factors.

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Step 3.2.1.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.2.1.1

Factor $4$ out of $32$ .

$k = \frac{2}{4 (8)} \cdot 4$

Step 3.2.1.2.1.2

Cancel the common factor.

$k = \frac{2}{4 \cdot 8} \cdot 4$

Step 3.2.1.2.1.3

Rewrite the expression.

$k = \frac{2}{8}$

Step 3.2.1.2.2

Cancel the common factor of $2$ and $8$ .

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Step 3.2.1.2.2.1

Factor $2$ out of $2$ .

$k = \frac{2 (1)}{8}$

Step 3.2.1.2.2.2

Cancel the common factors.

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Step 3.2.1.2.2.2.1

Factor $2$ out of $8$ .

$k = \frac{2 \cdot 1}{2 \cdot 4}$

Step 3.2.1.2.2.2.2

Cancel the common factor.

$k = \frac{2 \cdot 1}{2 \cdot 4}$

Step 3.2.1.2.2.2.3

Rewrite the expression.

$k = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{1}{4}$

Decimal Form:

$k = 0.25$