Algebra Examples

$\sqrt{9 x^{2}} \cdot \sqrt{9 y^{5}}$

Step 1

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

$\sqrt{{(3 x)}^{2}} \cdot \sqrt{9 y^{5}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$3 x \cdot \sqrt{9 y^{5}}$

Step 3

Rewrite $9 y^{5}$ as ${(3 y^{2})}^{2} y$ .

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Step 3.1

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

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

Step 3.2

Factor out $y^{4}$ .

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

Step 3.3

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

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

Step 3.4

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $3$ by $3$ .

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