Algebra Examples

$\sqrt{3 y^{2}} + 4 \sqrt{12 y^{2}} - y \sqrt{75}$

Step 1

Simplify each term.

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Step 1.1

Reorder $3$ and $y^{2}$ .

$\sqrt{y^{2} \cdot 3} + 4 \sqrt{12 y^{2}} - y \sqrt{75}$

Step 1.2

Pull terms out from under the radical.

$y \sqrt{3} + 4 \sqrt{12 y^{2}} - y \sqrt{75}$

Step 1.3

Rewrite $12 y^{2}$ as ${(2 y)}^{2} \cdot 3$ .

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Step 1.3.1

Factor $4$ out of $12$ .

$y \sqrt{3} + 4 \sqrt{4 (3) y^{2}} - y \sqrt{75}$

Step 1.3.2

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

$y \sqrt{3} + 4 \sqrt{2^{2} \cdot 3 y^{2}} - y \sqrt{75}$

Step 1.3.3

Move $3$ .

$y \sqrt{3} + 4 \sqrt{2^{2} y^{2} \cdot 3} - y \sqrt{75}$

Step 1.3.4

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

$y \sqrt{3} + 4 \sqrt{{(2 y)}^{2} \cdot 3} - y \sqrt{75}$

Step 1.4

Pull terms out from under the radical.

$y \sqrt{3} + 4 (2 y \sqrt{3}) - y \sqrt{75}$

Step 1.5

Multiply $2$ by $4$ .

$y \sqrt{3} + 8 (y \sqrt{3}) - y \sqrt{75}$

Step 1.6

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.6.1

Factor $25$ out of $75$ .

$y \sqrt{3} + 8 y \sqrt{3} - y \sqrt{25 (3)}$

Step 1.6.2

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

$y \sqrt{3} + 8 y \sqrt{3} - y \sqrt{5^{2} \cdot 3}$

Step 1.7

Pull terms out from under the radical.

$y \sqrt{3} + 8 y \sqrt{3} - y (5 \sqrt{3})$

Step 1.8

Multiply $5$ by $- 1$ .

$y \sqrt{3} + 8 y \sqrt{3} - 5 y \sqrt{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $y \sqrt{3}$ and $8 y \sqrt{3}$ .

$9 y \sqrt{3} - 5 y \sqrt{3}$

Step 2.2

Subtract $5 y \sqrt{3}$ from $9 y \sqrt{3}$ .

$4 y \sqrt{3}$