Algebra Examples

$\sqrt{6 x^{5} y^{4}} \cdot \sqrt{3 x^{2} y}$

Step 1

Rewrite $6 x^{5} y^{4}$ as ${(x^{2} y^{2})}^{2} \cdot (6 x)$ .

Tap for more steps...

Step 1.1

Factor out $x^{4}$ .

$\sqrt{6 (x^{4} x) y^{4}} \cdot \sqrt{3 x^{2} y}$

Step 1.2

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

$\sqrt{6 ({(x^{2})}^{2} x) y^{4}} \cdot \sqrt{3 x^{2} y}$

Step 1.3

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

$\sqrt{6 ({(x^{2})}^{2} x) {(y^{2})}^{2}} \cdot \sqrt{3 x^{2} y}$

Step 1.4

Move $x$ .

$\sqrt{6 ({(x^{2})}^{2}) {(y^{2})}^{2} x} \cdot \sqrt{3 x^{2} y}$

Step 1.5

Move $6$ .

$\sqrt{({(x^{2})}^{2}) {(y^{2})}^{2} \cdot 6 x} \cdot \sqrt{3 x^{2} y}$

Step 1.6

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

$\sqrt{{(x^{2} y^{2})}^{2} \cdot 6 x} \cdot \sqrt{3 x^{2} y}$

Step 1.7

Add parentheses.

$\sqrt{{(x^{2} y^{2})}^{2} \cdot (6 x)} \cdot \sqrt{3 x^{2} y}$

Step 2

Pull terms out from under the radical.

$x^{2} y^{2} \sqrt{6 x} \cdot \sqrt{3 x^{2} y}$

Step 3

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

Tap for more steps...

Step 3.1

Reorder $3$ and $x^{2}$ .

$x^{2} y^{2} \sqrt{6 x} \cdot \sqrt{x^{2} \cdot 3 y}$

Step 3.2

Add parentheses.

$x^{2} y^{2} \sqrt{6 x} \cdot \sqrt{x^{2} \cdot (3 y)}$

Step 4

Pull terms out from under the radical.

$x^{2} y^{2} \sqrt{6 x} \cdot (x \sqrt{3 y})$

Step 5

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $x$ .

$x \cdot x^{2} y^{2} \sqrt{6 x} \cdot \sqrt{3 y}$

Step 5.2

Multiply $x$ by $x^{2}$ .

Tap for more steps...

Step 5.2.1

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

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

Step 5.2.2

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

$x^{1 + 2} y^{2} \sqrt{6 x} \cdot \sqrt{3 y}$

Step 5.3

Add $1$ and $2$ .

$x^{3} y^{2} \sqrt{6 x} \cdot \sqrt{3 y}$

Step 6

Multiply $x^{3} y^{2} \sqrt{6 x} \sqrt{3 y}$ .

Tap for more steps...

Step 6.1

Combine using the product rule for radicals.

$x^{3} y^{2} \sqrt{3 y (6 x)}$

Step 6.2

Multiply $6$ by $3$ .

$x^{3} y^{2} \sqrt{18 y x}$

Step 7

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

Tap for more steps...

Step 7.1

Factor $9$ out of $18$ .

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

Step 7.2

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

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

Step 7.3

Add parentheses.

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

Step 7.4

Add parentheses.

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

Step 8

Pull terms out from under the radical.

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

Step 9

Rewrite using the commutative property of multiplication.

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