Basic Math Examples

$y \sqrt{z^{2} y^{3}} + 2 z \sqrt{y^{5}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $z^{2} y^{3}$ as ${(z y)}^{2} y$ .

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Step 1.1.1

Factor out $y^{2}$ .

$y \sqrt{z^{2} (y^{2} y)} + 2 z \sqrt{y^{5}}$

Step 1.1.2

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

$y \sqrt{{(z y)}^{2} y} + 2 z \sqrt{y^{5}}$

$y \sqrt{{(z y)}^{2} y} + 2 z \sqrt{y^{5}}$

Step 1.2

Pull terms out from under the radical.

$y (z y \sqrt{y}) + 2 z \sqrt{y^{5}}$

Step 1.3

Multiply $y$ by $y$ by adding the exponents.

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Step 1.3.1

Move $y$ .

$y \cdot y (z \sqrt{y}) + 2 z \sqrt{y^{5}}$

Step 1.3.2

Multiply $y$ by $y$ .

$y^{2} (z \sqrt{y}) + 2 z \sqrt{y^{5}}$

$y^{2} (z \sqrt{y}) + 2 z \sqrt{y^{5}}$

Step 1.4

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

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Step 1.4.1

Factor out $y^{4}$ .

$y^{2} (z \sqrt{y}) + 2 z \sqrt{y^{4} y}$

Step 1.4.2

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

$y^{2} (z \sqrt{y}) + 2 z \sqrt{{(y^{2})}^{2} y}$

$y^{2} (z \sqrt{y}) + 2 z \sqrt{{(y^{2})}^{2} y}$

Step 1.5

Pull terms out from under the radical.

$y^{2} (z \sqrt{y}) + 2 z y^{2} \sqrt{y}$

$y^{2} (z \sqrt{y}) + 2 z y^{2} \sqrt{y}$

Step 2

Simplify by adding terms.

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Step 2.1

Move $z$ .

$y^{2} z \sqrt{y} + 2 y^{2} z \sqrt{y}$

Step 2.2

Add $y^{2} z \sqrt{y}$ and $2 y^{2} z \sqrt{y}$ .

$3 y^{2} z \sqrt{y}$

$3 y^{2} z \sqrt{y}$

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