Pre-Algebra Examples

$(\sqrt{972 x y^{2}}) \sqrt{9 x}$

Step 1

Rewrite $972 x y^{2}$ as ${(18 y)}^{2} \cdot (3 x)$ .

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Step 1.1

Factor $324$ out of $972$ .

$\sqrt{324 (3) x y^{2}} \sqrt{9 x}$

Step 1.2

Rewrite $324$ as $18^{2}$ .

$\sqrt{18^{2} \cdot 3 x y^{2}} \sqrt{9 x}$

Step 1.3

Move $x$ .

$\sqrt{18^{2} \cdot 3 y^{2} x} \sqrt{9 x}$

Step 1.4

Move $3$ .

$\sqrt{18^{2} y^{2} \cdot 3 x} \sqrt{9 x}$

Step 1.5

Rewrite $18^{2} y^{2}$ as ${(18 y)}^{2}$ .

$\sqrt{{(18 y)}^{2} \cdot 3 x} \sqrt{9 x}$

Step 1.6

Add parentheses.

$\sqrt{{(18 y)}^{2} \cdot (3 x)} \sqrt{9 x}$

Step 2

Pull terms out from under the radical.

$18 y \sqrt{3 x} \sqrt{9 x}$

Step 3

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

$18 y \sqrt{3 x} \sqrt{3^{2} x}$

Step 4

Pull terms out from under the radical.

$18 y \sqrt{3 x} (3 \sqrt{x})$

Step 5

Multiply $18 y \sqrt{3 x} (3 \sqrt{x})$ .

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Step 5.1

Multiply $3$ by $18$ .

$54 y \sqrt{3 x} \sqrt{x}$

Step 5.2

Combine using the product rule for radicals.

$54 y \sqrt{x (3 x)}$

Step 5.3

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

$54 y \sqrt{3 (x^{1} x)}$

Step 5.4

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

$54 y \sqrt{3 (x^{1} x^{1})}$

Step 5.5

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

$54 y \sqrt{3 x^{1 + 1}}$

Step 5.6

Add $1$ and $1$ .

$54 y \sqrt{3 x^{2}}$

Step 6

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

$54 y \sqrt{x^{2} \cdot 3}$

Step 7

Pull terms out from under the radical.

$54 y x \sqrt{3}$