Algebra Examples

$\sqrt{6 a y} \cdot \sqrt{18 a} \cdot \frac{1}{y}$

Step 1

Rewrite $18 a$ as $3^{2} \cdot (2 a)$ .

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Step 1.1

Factor $9$ out of $18$ .

$\sqrt{6 a y} \cdot \sqrt{9 (2) a} \cdot \frac{1}{y}$

Step 1.2

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

$\sqrt{6 a y} \cdot \sqrt{3^{2} \cdot 2 a} \cdot \frac{1}{y}$

Step 1.3

Add parentheses.

$\sqrt{6 a y} \cdot \sqrt{3^{2} \cdot (2 a)} \cdot \frac{1}{y}$

Step 2

Pull terms out from under the radical.

$\sqrt{6 a y} \cdot (3 \sqrt{2 a}) \cdot \frac{1}{y}$

Step 3

Rewrite using the commutative property of multiplication.

$3 \sqrt{6 a y} \sqrt{2 a} \cdot \frac{1}{y}$

Step 4

Multiply $3 \sqrt{6 a y} \sqrt{2 a}$ .

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Step 4.1

Combine using the product rule for radicals.

$3 \sqrt{2 a (6 a y)} \cdot \frac{1}{y}$

Step 4.2

Multiply $6$ by $2$ .

$3 \sqrt{12 a (a y)} \cdot \frac{1}{y}$

Step 4.3

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

$3 \sqrt{12 (a^{1} a) y} \cdot \frac{1}{y}$

Step 4.4

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

$3 \sqrt{12 (a^{1} a^{1}) y} \cdot \frac{1}{y}$

Step 4.5

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

$3 \sqrt{12 a^{1 + 1} y} \cdot \frac{1}{y}$

Step 4.6

Add $1$ and $1$ .

$3 \sqrt{12 a^{2} y} \cdot \frac{1}{y}$

Step 5

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

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Step 5.1

Factor $4$ out of $12$ .

$3 \sqrt{4 (3) a^{2} y} \cdot \frac{1}{y}$

Step 5.2

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

$3 \sqrt{2^{2} \cdot 3 a^{2} y} \cdot \frac{1}{y}$

Step 5.3

Move $3$ .

$3 \sqrt{2^{2} a^{2} \cdot 3 y} \cdot \frac{1}{y}$

Step 5.4

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

$3 \sqrt{{(2 a)}^{2} \cdot 3 y} \cdot \frac{1}{y}$

Step 5.5

Add parentheses.

$3 \sqrt{{(2 a)}^{2} \cdot (3 y)} \cdot \frac{1}{y}$

Step 6

Pull terms out from under the radical.

$3 (2 a \sqrt{3 y}) \cdot \frac{1}{y}$

Step 7

Multiply $2$ by $3$ .

$6 (a \sqrt{3 y}) \cdot \frac{1}{y}$

Step 8

Multiply $6 a \sqrt{3 y} \frac{1}{y}$ .

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Step 8.1

Combine $6$ and $\frac{1}{y}$ .

$a \sqrt{3 y} \frac{6}{y}$

Step 8.2

Combine $\frac{6}{y}$ and $a$ .

$\frac{6 a}{y} \sqrt{3 y}$

Step 8.3

Combine $\frac{6 a}{y}$ and $\sqrt{3 y}$ .

$\frac{6 a \sqrt{3 y}}{y}$