Algebra Examples

$\sqrt{3 x y} - 2 \sqrt{27 x^{3} y} + 4 \sqrt{3 x y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27 x^{3} y$ as ${(3 x)}^{2} \cdot (3 x y)$ .

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Step 1.1.1

Factor $9$ out of $27$ .

$\sqrt{3 x y} - 2 \sqrt{9 (3) x^{3} y} + 4 \sqrt{3 x y}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

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

Step 1.1.3

Factor out $x^{2}$ .

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

Step 1.1.4

Move $3$ .

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

Step 1.1.5

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

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

Step 1.1.6

Add parentheses.

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

Step 1.1.7

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $3$ by $- 2$ .

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

Step 2

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

$- 6 x \sqrt{3 x y} + 5 \sqrt{3 x y}$