Algebra Examples

$4 \sqrt{2 x} \cdot 5 \sqrt{6 x y^{2}}$

Step 1

Multiply $5$ by $4$ .

$20 \sqrt{2 x} \sqrt{6 x y^{2}}$

Step 2

Rewrite $6 x y^{2}$ as $y^{2} \cdot (6 x)$ .

Tap for more steps...

Step 2.1

Move $x$ .

$20 \sqrt{2 x} \sqrt{6 y^{2} x}$

Step 2.2

Reorder $6$ and $y^{2}$ .

$20 \sqrt{2 x} \sqrt{y^{2} \cdot 6 x}$

Step 2.3

Add parentheses.

$20 \sqrt{2 x} \sqrt{y^{2} \cdot (6 x)}$

Step 3

Pull terms out from under the radical.

$20 \sqrt{2 x} (| y | \sqrt{6 x})$

Step 4

Multiply $20 \sqrt{2 x} (| y | \sqrt{6 x})$ .

Tap for more steps...

Step 4.1

Combine using the product rule for radicals.

$20 \sqrt{6 x (2 x)} | y |$

Step 4.2

Multiply $2$ by $6$ .

$20 \sqrt{12 x \cdot x} | y |$

Step 4.3

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

$20 \sqrt{12 (x^{1} x)} | y |$

Step 4.4

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

$20 \sqrt{12 (x^{1} x^{1})} | y |$

Step 4.5

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

$20 \sqrt{12 x^{1 + 1}} | y |$

Step 4.6

Add $1$ and $1$ .

$20 \sqrt{12 x^{2}} | y |$

Step 5

Rewrite $12 x^{2}$ as ${(2 x)}^{2} \cdot 3$ .

Tap for more steps...

Step 5.1

Factor $4$ out of $12$ .

$20 \sqrt{4 (3) x^{2}} | y |$

Step 5.2

Rewrite $4$ as $2^{2}$ .

$20 \sqrt{2^{2} \cdot 3 x^{2}} | y |$

Step 5.3

Move $3$ .

$20 \sqrt{2^{2} x^{2} \cdot 3} | y |$

Step 5.4

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

$20 \sqrt{{(2 x)}^{2} \cdot 3} | y |$

Step 6

Pull terms out from under the radical.

$20 (| 2 x | \sqrt{3}) | y |$

Step 7

Remove non-negative terms from the absolute value.

$20 (2 | x | \sqrt{3}) | y |$

Step 8

Multiply $2$ by $20$ .

$40 (| x | \sqrt{3}) | y |$

Step 9

To multiply absolute values, multiply the terms inside each absolute value.

$40 | y x | \sqrt{3}$