Algebra Examples

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

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

27 x^{3} y

$27 x^{3} y$ as

{(3 x)}^{2} \cdot (3 x y)

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

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Step 1.1.1

Factor

9

$9$ out of

27

$27$ .

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

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

Step 1.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

Step 1.1.3

Factor out

x^{2}

$x^{2}$ .

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

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

Step 1.1.4

Move

3

$3$ .

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

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

Step 1.1.5

Rewrite

3^{2} x^{2}

$3^{2} x^{2}$ as

{(3 x)}^{2}

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

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

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

Step 1.1.6

Add parentheses.

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

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

Step 1.1.7

Add parentheses.

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

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

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 1.3

Rewrite

48 x y

$48 x y$ as

{(2^{2})}^{2} \cdot (3 x y)

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

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Step 1.3.1

Factor

16

$16$ out of

48

$48$ .

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

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

Step 1.3.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

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

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

Step 1.3.3

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 1.3.4

Add parentheses.

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

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

Step 1.3.5

Add parentheses.

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

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

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

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

Step 1.4

Pull terms out from under the radical.

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

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

Step 1.5

Rewrite using the commutative property of multiplication.

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

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

Step 1.6

Raise

2

$2$ to the power of

2

$2$ .

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

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

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

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

Step 2

Add

3 x \sqrt{3 x y}

$3 x \sqrt{3 x y}$ and

4 x \sqrt{3 x y}

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

7 x \sqrt{3 x y}

$7 x \sqrt{3 x y}$