Algebra Examples

$6 \sqrt{4 x^{2}} \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 1

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

$6 \sqrt{{(2 x)}^{2}} \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 2

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

$6 (2 x) \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 3

Multiply $2$ by $6$ .

$12 x \cdot (2 \sqrt{9 x^{2} y^{2}})$

Step 4

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

$12 x \cdot (2 \sqrt{{(3 x y)}^{2}})$

Step 5

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

$12 x \cdot (2 (3 x y))$

Step 6

Multiply $x$ by $x$ by adding the exponents.

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Step 6.1

Move $x$ .

$12 (x \cdot x) \cdot (2 (3 y))$

Step 6.2

Multiply $x$ by $x$ .

$12 x^{2} \cdot (2 (3 y))$

Step 7

Multiply $3$ by $2$ .

$12 x^{2} \cdot (6 y)$

Step 8

Rewrite using the commutative property of multiplication.

$12 \cdot 6 x^{2} y$

Step 9

Multiply $12$ by $6$ .

$72 x^{2} y$