Algebra Examples

$\sqrt{14 x y} \cdot \sqrt{12} \cdot \sqrt{30 y}$

Step 1

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

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Step 1.1

Factor $4$ out of $12$ .

$\sqrt{14 x y} \cdot \sqrt{4 (3)} \cdot \sqrt{30 y}$

Step 1.2

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

$\sqrt{14 x y} \cdot \sqrt{2^{2} \cdot 3} \cdot \sqrt{30 y}$

Step 2

Pull terms out from under the radical.

$\sqrt{14 x y} \cdot (2 \sqrt{3}) \cdot \sqrt{30 y}$

Step 3

Multiply $\sqrt{14 x y} (2 \sqrt{3})$ .

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Step 3.1

Combine using the product rule for radicals.

$2 \sqrt{14 x y \cdot 3} \cdot \sqrt{30 y}$

Step 3.2

Multiply $3$ by $14$ .

$2 \sqrt{42 x y} \cdot \sqrt{30 y}$

Step 4

Multiply $2 \sqrt{42 x y} \sqrt{30 y}$ .

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Step 4.1

Combine using the product rule for radicals.

$2 \sqrt{30 y (42 x y)}$

Step 4.2

Multiply $42$ by $30$ .

$2 \sqrt{1260 y (x y)}$

Step 4.3

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

$2 \sqrt{1260 (x (y^{1} y))}$

Step 4.4

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

$2 \sqrt{1260 (x (y^{1} y^{1}))}$

Step 4.5

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

$2 \sqrt{1260 (x y^{1 + 1})}$

Step 4.6

Add $1$ and $1$ .

$2 \sqrt{1260 (x y^{2})}$

Step 5

Rewrite $1260 x y^{2}$ as ${(6 y)}^{2} \cdot (35 x)$ .

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Step 5.1

Factor $36$ out of $1260$ .

$2 \sqrt{36 (35) x y^{2}}$

Step 5.2

Rewrite $36$ as $6^{2}$ .

$2 \sqrt{6^{2} \cdot 35 x y^{2}}$

Step 5.3

Move $x$ .

$2 \sqrt{6^{2} \cdot 35 y^{2} x}$

Step 5.4

Move $35$ .

$2 \sqrt{6^{2} y^{2} \cdot 35 x}$

Step 5.5

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

$2 \sqrt{{(6 y)}^{2} \cdot 35 x}$

Step 5.6

Add parentheses.

$2 \sqrt{{(6 y)}^{2} \cdot (35 x)}$

Step 6

Pull terms out from under the radical.

$2 (6 y \sqrt{35 x})$

Step 7

Multiply $6$ by $2$ .

$12 y \sqrt{35 x}$