Basic Math Examples

$V = 30 \cdot \sqrt{\frac{210}{120}}$

Step 1

Cancel the common factor of $210$ and $120$ .

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Step 1.1

Factor $30$ out of $210$ .

$V = 30 \cdot \sqrt{\frac{30 (7)}{120}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $30$ out of $120$ .

$V = 30 \cdot \sqrt{\frac{30 \cdot 7}{30 \cdot 4}}$

Step 1.2.2

Cancel the common factor.

$V = 30 \cdot \sqrt{\frac{30 \cdot 7}{30 \cdot 4}}$

Step 1.2.3

Rewrite the expression.

$V = 30 \cdot \sqrt{\frac{7}{4}}$

Step 2

Rewrite $\sqrt{\frac{7}{4}}$ as $\frac{\sqrt{7}}{\sqrt{4}}$ .

$V = 30 \cdot \frac{\sqrt{7}}{\sqrt{4}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$V = 30 \cdot \frac{\sqrt{7}}{\sqrt{2^{2}}}$

Step 3.2

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

$V = 30 \cdot \frac{\sqrt{7}}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $30$ .

$V = 2 (15) \cdot \frac{\sqrt{7}}{2}$

Step 4.2

Cancel the common factor.

$V = 2 \cdot 15 \cdot \frac{\sqrt{7}}{2}$

Step 4.3

Rewrite the expression.

$V = 15 \cdot \sqrt{7}$

$V = 15 \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$V = 15 \sqrt{7}$

Decimal Form:

$V = 39.68626966 \dots$