Algebra Examples

$\sqrt{27 x y} \cdot \sqrt{9 x y^{2}}$

Step 1

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

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Step 1.1

Factor $9$ out of $27$ .

$\sqrt{9 (3) x y} \cdot \sqrt{9 x y^{2}}$

Step 1.2

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

$\sqrt{3^{2} \cdot 3 x y} \cdot \sqrt{9 x y^{2}}$

Step 1.3

Add parentheses.

$\sqrt{3^{2} \cdot 3 (x y)} \cdot \sqrt{9 x y^{2}}$

Step 1.4

Add parentheses.

$\sqrt{3^{2} \cdot (3 x y)} \cdot \sqrt{9 x y^{2}}$

Step 2

Pull terms out from under the radical.

$3 \sqrt{3 x y} \cdot \sqrt{9 x y^{2}}$

Step 3

Rewrite $9 x y^{2}$ as ${(3 y)}^{2} x$ .

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Step 3.1

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

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

Step 3.2

Move $x$ .

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

Step 3.3

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

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

Step 4

Pull terms out from under the radical.

$3 \sqrt{3 x y} \cdot (3 y \sqrt{x})$

Step 5

Multiply $3 \sqrt{3 x y} (3 y \sqrt{x})$ .

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Step 5.1

Multiply $3$ by $3$ .

$9 \sqrt{3 x y} (y \sqrt{x})$

Step 5.2

Combine using the product rule for radicals.

$9 (y \sqrt{3 x y x})$

Step 5.3

Raise $x$ to the power of $1$ .

$9 (y \sqrt{3 (x^{1} x) y})$

Step 5.4

Raise $x$ to the power of $1$ .

$9 (y \sqrt{3 (x^{1} x^{1}) y})$

Step 5.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 (y \sqrt{3 x^{1 + 1} y})$

Step 5.6

Add $1$ and $1$ .

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

Step 6

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

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Step 6.1

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

$9 (y \sqrt{x^{2} \cdot 3 y})$

Step 6.2

Add parentheses.

$9 (y \sqrt{x^{2} \cdot (3 y)})$

Step 7

Pull terms out from under the radical.

$9 (y (x \sqrt{3 y}))$

Step 8

Reorder factors in $9 y (x \sqrt{3 y})$ .

$9 y x \sqrt{3 y}$