Basic Math Examples

$\sqrt{5 y^{2}} - 5 \sqrt{125 y^{2}} - 6 \sqrt{125 y^{2}}$

Step 1

Simplify each term.

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Step 1.1

Reorder $5$ and $y^{2}$ .

$\sqrt{y^{2} \cdot 5} - 5 \sqrt{125 y^{2}} - 6 \sqrt{125 y^{2}}$

Step 1.2

Pull terms out from under the radical.

$y \sqrt{5} - 5 \sqrt{125 y^{2}} - 6 \sqrt{125 y^{2}}$

Step 1.3

Rewrite $125 y^{2}$ as ${(5 y)}^{2} \cdot 5$ .

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Step 1.3.1

Factor $25$ out of $125$ .

$y \sqrt{5} - 5 \sqrt{25 (5) y^{2}} - 6 \sqrt{125 y^{2}}$

Step 1.3.2

Rewrite $25$ as $5^{2}$ .

$y \sqrt{5} - 5 \sqrt{5^{2} \cdot 5 y^{2}} - 6 \sqrt{125 y^{2}}$

Step 1.3.3

Move $5$ .

$y \sqrt{5} - 5 \sqrt{5^{2} y^{2} \cdot 5} - 6 \sqrt{125 y^{2}}$

Step 1.3.4

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

$y \sqrt{5} - 5 \sqrt{{(5 y)}^{2} \cdot 5} - 6 \sqrt{125 y^{2}}$

Step 1.4

Pull terms out from under the radical.

$y \sqrt{5} - 5 (5 y \sqrt{5}) - 6 \sqrt{125 y^{2}}$

Step 1.5

Multiply $5$ by $- 5$ .

$y \sqrt{5} - 25 (y \sqrt{5}) - 6 \sqrt{125 y^{2}}$

Step 1.6

Rewrite $125 y^{2}$ as ${(5 y)}^{2} \cdot 5$ .

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Step 1.6.1

Factor $25$ out of $125$ .

$y \sqrt{5} - 25 y \sqrt{5} - 6 \sqrt{25 (5) y^{2}}$

Step 1.6.2

Rewrite $25$ as $5^{2}$ .

$y \sqrt{5} - 25 y \sqrt{5} - 6 \sqrt{5^{2} \cdot 5 y^{2}}$

Step 1.6.3

Move $5$ .

$y \sqrt{5} - 25 y \sqrt{5} - 6 \sqrt{5^{2} y^{2} \cdot 5}$

Step 1.6.4

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

$y \sqrt{5} - 25 y \sqrt{5} - 6 \sqrt{{(5 y)}^{2} \cdot 5}$

Step 1.7

Pull terms out from under the radical.

$y \sqrt{5} - 25 y \sqrt{5} - 6 (5 y \sqrt{5})$

Step 1.8

Multiply $5$ by $- 6$ .

$y \sqrt{5} - 25 y \sqrt{5} - 30 y \sqrt{5}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $25 y \sqrt{5}$ from $y \sqrt{5}$ .

$- 24 y \sqrt{5} - 30 y \sqrt{5}$

Step 2.2

Subtract $30 y \sqrt{5}$ from $- 24 y \sqrt{5}$ .

$- 54 y \sqrt{5}$