Basic Math Examples

$\sqrt{243 y^{3}} + 4 y \sqrt{3 y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $243 y^{3}$ as ${(9 y)}^{2} \cdot (3 y)$ .

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Step 1.1.1

Factor $81$ out of $243$ .

$\sqrt{81 (3) y^{3}} + 4 y \sqrt{3 y}$

Step 1.1.2

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} \cdot 3 y^{3}} + 4 y \sqrt{3 y}$

Step 1.1.3

Factor out $y^{2}$ .

$\sqrt{9^{2} \cdot 3 (y^{2} y)} + 4 y \sqrt{3 y}$

Step 1.1.4

Move $3$ .

$\sqrt{9^{2} y^{2} \cdot 3 y} + 4 y \sqrt{3 y}$

Step 1.1.5

Rewrite $9^{2} y^{2}$ as ${(9 y)}^{2}$ .

$\sqrt{{(9 y)}^{2} \cdot 3 y} + 4 y \sqrt{3 y}$

Step 1.1.6

Add parentheses.

$\sqrt{{(9 y)}^{2} \cdot (3 y)} + 4 y \sqrt{3 y}$

$\sqrt{{(9 y)}^{2} \cdot (3 y)} + 4 y \sqrt{3 y}$

Step 1.2

Pull terms out from under the radical.

$9 y \sqrt{3 y} + 4 y \sqrt{3 y}$

$9 y \sqrt{3 y} + 4 y \sqrt{3 y}$

Step 2

Add $9 y \sqrt{3 y}$ and $4 y \sqrt{3 y}$ .

$13 y \sqrt{3 y}$

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