Algebra Examples

$\sqrt{27 x^{5} y} - 6 \sqrt{3 x^{5} y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27 x^{5} y$ as ${(3 x^{2})}^{2} \cdot (3 x y)$ .

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Step 1.1.1

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{5} y} - 6 \sqrt{3 x^{5} y}$

Step 1.1.2

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

$\sqrt{3^{2} \cdot 3 x^{5} y} - 6 \sqrt{3 x^{5} y}$

Step 1.1.3

Factor out $x^{4}$ .

$\sqrt{3^{2} \cdot 3 (x^{4} x) y} - 6 \sqrt{3 x^{5} y}$

Step 1.1.4

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

$\sqrt{3^{2} \cdot 3 ({(x^{2})}^{2} x) y} - 6 \sqrt{3 x^{5} y}$

Step 1.1.5

Move $3$ .

$\sqrt{3^{2} {(x^{2})}^{2} \cdot 3 x y} - 6 \sqrt{3 x^{5} y}$

Step 1.1.6

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

$\sqrt{{(3 x^{2})}^{2} \cdot 3 x y} - 6 \sqrt{3 x^{5} y}$

Step 1.1.7

Add parentheses.

$\sqrt{{(3 x^{2})}^{2} \cdot 3 (x y)} - 6 \sqrt{3 x^{5} y}$

Step 1.1.8

Add parentheses.

$\sqrt{{(3 x^{2})}^{2} \cdot (3 x y)} - 6 \sqrt{3 x^{5} y}$

Step 1.2

Pull terms out from under the radical.

$3 x^{2} \sqrt{3 x y} - 6 \sqrt{3 x^{5} y}$

Step 1.3

Rewrite $3 x^{5} y$ as ${(x^{2})}^{2} \cdot (3 x y)$ .

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Step 1.3.1

Factor out $x^{4}$ .

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

Step 1.3.2

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

$3 x^{2} \sqrt{3 x y} - 6 \sqrt{3 ({(x^{2})}^{2} x) y}$

Step 1.3.3

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

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

Step 1.3.4

Add parentheses.

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

Step 1.3.5

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

$3 x^{2} \sqrt{3 x y} - 6 x^{2} \sqrt{3 x y}$

Step 2

Subtract $6 x^{2} \sqrt{3 x y}$ from $3 x^{2} \sqrt{3 x y}$ .

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