Basic Math Examples

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

Step 1

Add ${(- 5 y)}^{2}$ and ${(- 5 y)}^{2}$ .

$\sqrt{2 {(- 5 y)}^{2} - 5 y}$

Step 2

Let $u = y$ . Substitute $u$ for all occurrences of $y$ .

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Step 2.1

Apply the product rule to $- 5 u$ .

$\sqrt{2 ({(- 5)}^{2} u^{2}) - 5 u}$

Step 2.2

Raise $- 5$ to the power of $2$ .

$\sqrt{2 (25 u^{2}) - 5 u}$

Step 2.3

Multiply $25$ by $2$ .

$\sqrt{50 u^{2} - 5 u}$

$\sqrt{50 u^{2} - 5 u}$

Step 3

Factor $5 u$ out of $50 u^{2} - 5 u$ .

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Step 3.1

Factor $5 u$ out of $50 u^{2}$ .

$\sqrt{5 u (10 u) - 5 u}$

Step 3.2

Factor $5 u$ out of $- 5 u$ .

$\sqrt{5 u (10 u) + 5 u (- 1)}$

Step 3.3

Factor $5 u$ out of $5 u (10 u) + 5 u (- 1)$ .

$\sqrt{5 u (10 u - 1)}$

$\sqrt{5 u (10 u - 1)}$

Step 4

Replace all occurrences of $u$ with $y$ .

$\sqrt{5 y (10 y - 1)}$

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