Finite Math Examples

$\frac{\sqrt{28 y^{5}}}{\sqrt{7} y}$

Step 1

Combine $\sqrt{28 y^{5}}$ and $\sqrt{7}$ into a single radical.

$\frac{\sqrt{\frac{28 y^{5}}{7}}}{y}$

Step 2

Cancel the common factor of $28$ and $7$ .

Tap for more steps...

Step 2.1

Factor $7$ out of $28 y^{5}$ .

$\frac{\sqrt{\frac{7 (4 y^{5})}{7}}}{y}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $7$ out of $7$ .

$\frac{\sqrt{\frac{7 (4 y^{5})}{7 (1)}}}{y}$

Step 2.2.2

Cancel the common factor.

$\frac{\sqrt{\frac{7 (4 y^{5})}{7 \cdot 1}}}{y}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{\frac{4 y^{5}}{1}}}{y}$

Step 2.2.4

Divide $4 y^{5}$ by $1$ .

$\frac{\sqrt{4 y^{5}}}{y}$

$\frac{\sqrt{4 y^{5}}}{y}$

$\frac{\sqrt{4 y^{5}}}{y}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Rewrite $4 y^{5}$ as ${(2 y^{2})}^{2} y$ .

Tap for more steps...

Step 3.1.1

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

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

Step 3.1.2

Factor out $y^{4}$ .

$\frac{\sqrt{2^{2} (y^{4} y)}}{y}$

Step 3.1.3

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\frac{\sqrt{2^{2} ({(y^{2})}^{2} y)}}{y}$

Step 3.1.4

Rewrite $2^{2} {(y^{2})}^{2}$ as ${(2 y^{2})}^{2}$ .

$\frac{\sqrt{{(2 y^{2})}^{2} y}}{y}$

$\frac{\sqrt{{(2 y^{2})}^{2} y}}{y}$

Step 3.2

Pull terms out from under the radical.

$\frac{2 y^{2} \sqrt{y}}{y}$

$\frac{2 y^{2} \sqrt{y}}{y}$

Step 4

Cancel the common factor of $y^{2}$ and $y$ .

Tap for more steps...

Step 4.1

Factor $y$ out of $2 y^{2} \sqrt{y}$ .

$\frac{y (2 y \sqrt{y})}{y}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Raise $y$ to the power of $1$ .

$\frac{y (2 y \sqrt{y})}{y^{1}}$

Step 4.2.2

Factor $y$ out of $y^{1}$ .

$\frac{y (2 y \sqrt{y})}{y \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{y (2 y \sqrt{y})}{y \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{2 y \sqrt{y}}{1}$

Step 4.2.5

Divide $2 y \sqrt{y}$ by $1$ .

$2 y \sqrt{y}$

$2 y \sqrt{y}$

$2 y \sqrt{y}$

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