Basic Math Examples

$\sqrt{48 y^{2}} + 3 y \sqrt{12} - \sqrt{108 y^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $48 y^{2}$ as ${(4 y)}^{2} \cdot 3$ .

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Step 1.1.1

Factor $16$ out of $48$ .

$\sqrt{16 (3) y^{2}} + 3 y \sqrt{12} - \sqrt{108 y^{2}}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 3 y^{2}} + 3 y \sqrt{12} - \sqrt{108 y^{2}}$

Step 1.1.3

Move $3$ .

$\sqrt{4^{2} y^{2} \cdot 3} + 3 y \sqrt{12} - \sqrt{108 y^{2}}$

Step 1.1.4

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

$\sqrt{{(4 y)}^{2} \cdot 3} + 3 y \sqrt{12} - \sqrt{108 y^{2}}$

Step 1.2

Pull terms out from under the radical.

$4 y \sqrt{3} + 3 y \sqrt{12} - \sqrt{108 y^{2}}$

Step 1.3

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

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Step 1.3.1

Factor $4$ out of $12$ .

$4 y \sqrt{3} + 3 y \sqrt{4 (3)} - \sqrt{108 y^{2}}$

Step 1.3.2

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

$4 y \sqrt{3} + 3 y \sqrt{2^{2} \cdot 3} - \sqrt{108 y^{2}}$

Step 1.4

Pull terms out from under the radical.

$4 y \sqrt{3} + 3 y (2 \sqrt{3}) - \sqrt{108 y^{2}}$

Step 1.5

Multiply $2$ by $3$ .

$4 y \sqrt{3} + 6 y \sqrt{3} - \sqrt{108 y^{2}}$

Step 1.6

Rewrite $108 y^{2}$ as ${(6 y)}^{2} \cdot 3$ .

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Step 1.6.1

Factor $36$ out of $108$ .

$4 y \sqrt{3} + 6 y \sqrt{3} - \sqrt{36 (3) y^{2}}$

Step 1.6.2

Rewrite $36$ as $6^{2}$ .

$4 y \sqrt{3} + 6 y \sqrt{3} - \sqrt{6^{2} \cdot 3 y^{2}}$

Step 1.6.3

Move $3$ .

$4 y \sqrt{3} + 6 y \sqrt{3} - \sqrt{6^{2} y^{2} \cdot 3}$

Step 1.6.4

Rewrite $6^{2} y^{2}$ as ${(6 y)}^{2}$ .

$4 y \sqrt{3} + 6 y \sqrt{3} - \sqrt{{(6 y)}^{2} \cdot 3}$

Step 1.7

Pull terms out from under the radical.

$4 y \sqrt{3} + 6 y \sqrt{3} - (6 y \sqrt{3})$

Step 1.8

Multiply $6$ by $- 1$ .

$4 y \sqrt{3} + 6 y \sqrt{3} - 6 y \sqrt{3}$

Step 2

Combine the opposite terms in $4 y \sqrt{3} + 6 y \sqrt{3} - 6 y \sqrt{3}$ .

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Step 2.1

Subtract $6 y \sqrt{3}$ from $6 y \sqrt{3}$ .

$4 y \sqrt{3} + 0$

Step 2.2

Add $4 y \sqrt{3}$ and $0$ .

$4 y \sqrt{3}$