Linear Algebra Examples

$\frac{\sqrt{25 (100 - 25)}}{1250}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Subtract $25$ from $100$ .

$\frac{\sqrt{25 \cdot 75}}{1250}$

Step 1.2

Multiply $25$ by $75$ .

$\frac{\sqrt{1875}}{1250}$

Step 1.3

Rewrite $1875$ as $25^{2} \cdot 3$ .

Tap for more steps...

Step 1.3.1

Factor $625$ out of $1875$ .

$\frac{\sqrt{625 (3)}}{1250}$

Step 1.3.2

Rewrite $625$ as $25^{2}$ .

$\frac{\sqrt{25^{2} \cdot 3}}{1250}$

$\frac{\sqrt{25^{2} \cdot 3}}{1250}$

Step 1.4

Pull terms out from under the radical.

$\frac{25 \sqrt{3}}{1250}$

$\frac{25 \sqrt{3}}{1250}$

Step 2

Cancel the common factor of $25$ and $1250$ .

Tap for more steps...

Step 2.1

Factor $25$ out of $25 \sqrt{3}$ .

$\frac{25 (\sqrt{3})}{1250}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $25$ out of $1250$ .

$\frac{25 \sqrt{3}}{25 \cdot 50}$

Step 2.2.2

Cancel the common factor.

$\frac{25 \sqrt{3}}{25 \cdot 50}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{3}}{50}$

$\frac{\sqrt{3}}{50}$

$\frac{\sqrt{3}}{50}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{50}$

Decimal Form:

$0.03464101 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$