Algebra Examples

$\sqrt{27 x^{3} y} + x \sqrt{48 x y}$

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 $27$ .

$\sqrt{9 (3) x^{3} y} + x \sqrt{48 x y}$

Step 1.1.2

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

$\sqrt{3^{2} \cdot 3 x^{3} y} + x \sqrt{48 x y}$

Step 1.1.3

Factor out $x^{2}$ .

$\sqrt{3^{2} \cdot 3 (x^{2} x) y} + x \sqrt{48 x y}$

Step 1.1.4

Move $3$ .

$\sqrt{3^{2} x^{2} \cdot 3 x y} + x \sqrt{48 x y}$

Step 1.1.5

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

$\sqrt{{(3 x)}^{2} \cdot 3 x y} + x \sqrt{48 x y}$

Step 1.1.6

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot 3 (x y)} + x \sqrt{48 x y}$

Step 1.1.7

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot (3 x y)} + x \sqrt{48 x y}$

Step 1.2

Pull terms out from under the radical.

$3 x \sqrt{3 x y} + x \sqrt{48 x y}$

Step 1.3

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

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Step 1.3.1

Factor $16$ out of $48$ .

$3 x \sqrt{3 x y} + x \sqrt{16 (3) x y}$

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.3.4

Add parentheses.

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

Step 1.3.5

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Rewrite using the commutative property of multiplication.

$3 x \sqrt{3 x y} + 2^{2} x \sqrt{3 x y}$

Step 1.6

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

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

Step 2

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

$7 x \sqrt{3 x y}$