Linear Algebra Examples

$\sqrt{\frac{52}{100}}$

Step 1

Cancel the common factor of $52$ and $100$ .

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Step 1.1

Factor $4$ out of $52$ .

$\sqrt{\frac{4 (13)}{100}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $100$ .

$\sqrt{\frac{4 \cdot 13}{4 \cdot 25}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{\frac{4 \cdot 13}{4 \cdot 25}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{\frac{13}{25}}$

Step 2

Rewrite $\sqrt{\frac{13}{25}}$ as $\frac{\sqrt{13}}{\sqrt{25}}$ .

$\frac{\sqrt{13}}{\sqrt{25}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt{13}}{\sqrt{5^{2}}}$

Step 3.2

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

$\frac{\sqrt{13}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{13}}{5}$

Decimal Form:

$0.72111025 \dots$