Algebra Examples

$y \sqrt[4]{32 x^{6}} + \sqrt[4]{162 x^{2} y^{4}}$

Step 1

Rewrite $32 x^{6}$ as ${(2 x)}^{4} \cdot (2 x^{2})$ .

Tap for more steps...

Step 1.1

Factor $16$ out of $32$ .

$y \sqrt[4]{16 (2) x^{6}} + \sqrt[4]{162 x^{2} y^{4}}$

Step 1.2

Rewrite $16$ as $2^{4}$ .

$y \sqrt[4]{2^{4} \cdot 2 x^{6}} + \sqrt[4]{162 x^{2} y^{4}}$

Step 1.3

Factor out $x^{4}$ .

$y \sqrt[4]{2^{4} \cdot 2 (x^{4} x^{2})} + \sqrt[4]{162 x^{2} y^{4}}$

Step 1.4

Move $2$ .

$y \sqrt[4]{2^{4} x^{4} \cdot 2 x^{2}} + \sqrt[4]{162 x^{2} y^{4}}$

Step 1.5

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

$y \sqrt[4]{{(2 x)}^{4} \cdot 2 x^{2}} + \sqrt[4]{162 x^{2} y^{4}}$

Step 1.6

Add parentheses.

$y \sqrt[4]{{(2 x)}^{4} \cdot (2 x^{2})} + \sqrt[4]{162 x^{2} y^{4}}$

Step 2

Pull terms out from under the radical.

$y (2 x \sqrt[4]{2 x^{2}}) + \sqrt[4]{162 x^{2} y^{4}}$

Step 3

Rewrite using the commutative property of multiplication.

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{162 x^{2} y^{4}}$

Step 4

Rewrite $162 x^{2} y^{4}$ as ${(3 y)}^{4} \cdot (2 x^{2})$ .

Tap for more steps...

Step 4.1

Factor $81$ out of $162$ .

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{81 (2) x^{2} y^{4}}$

Step 4.2

Rewrite $81$ as $3^{4}$ .

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{3^{4} \cdot 2 x^{2} y^{4}}$

Step 4.3

Move $x^{2}$ .

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{3^{4} \cdot 2 y^{4} x^{2}}$

Step 4.4

Move $2$ .

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{3^{4} y^{4} \cdot 2 x^{2}}$

Step 4.5

Rewrite $3^{4} y^{4}$ as ${(3 y)}^{4}$ .

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{{(3 y)}^{4} \cdot 2 x^{2}}$

Step 4.6

Add parentheses.

$2 y x \sqrt[4]{2 x^{2}} + \sqrt[4]{{(3 y)}^{4} \cdot (2 x^{2})}$

Step 5

Pull terms out from under the radical.

$2 y x \sqrt[4]{2 x^{2}} + 3 y \sqrt[4]{2 x^{2}}$