Simplify y square root of 2y^3-3 square root of 8y^5+3y square root of 72y^3

$y \sqrt{2 y^{3}} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Step 1

Simplify each term.

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

Factor out $y^{2}$ .

$y \sqrt{2 (y^{2} y)} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

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

$y \sqrt{y^{2} \cdot 2 y} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Add parentheses.

$y \sqrt{y^{2} \cdot (2 y)} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Pull terms out from under the radical.

$y (y \sqrt{2 y}) - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$y \cdot y \sqrt{2 y} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Multiply $y$ by $y$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{8 y^{5}} + 3 y \sqrt{72 y^{3}}$

Rewrite $8 y^{5}$ as ${(2 y^{2})}^{2} \cdot (2 y)$ .

Factor $4$ out of $8$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{4 (2) y^{5}} + 3 y \sqrt{72 y^{3}}$

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

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} \cdot 2 y^{5}} + 3 y \sqrt{72 y^{3}}$

Factor out $y^{4}$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} \cdot 2 (y^{4} y)} + 3 y \sqrt{72 y^{3}}$

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

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} \cdot 2 ({(y^{2})}^{2} y)} + 3 y \sqrt{72 y^{3}}$

Move $2$ .

$y^{2} \sqrt{2 y} - 3 \sqrt{2^{2} {(y^{2})}^{2} \cdot 2 y} + 3 y \sqrt{72 y^{3}}$

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

$y^{2} \sqrt{2 y} - 3 \sqrt{{(2 y^{2})}^{2} \cdot 2 y} + 3 y \sqrt{72 y^{3}}$

Add parentheses.

$y^{2} \sqrt{2 y} - 3 \sqrt{{(2 y^{2})}^{2} \cdot (2 y)} + 3 y \sqrt{72 y^{3}}$

Pull terms out from under the radical.

$y^{2} \sqrt{2 y} - 3 (2 y^{2} \sqrt{2 y}) + 3 y \sqrt{72 y^{3}}$

Multiply $2$ by $- 3$ .

$y^{2} \sqrt{2 y} - 6 (y^{2} \sqrt{2 y}) + 3 y \sqrt{72 y^{3}}$

Rewrite $72 y^{3}$ as ${(6 y)}^{2} \cdot (2 y)$ .

Factor $36$ out of $72$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 3 y \sqrt{36 (2) y^{3}}$

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

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

Factor out $y^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $6$ by $3$ .

$y^{2} \sqrt{2 y} - 6 y^{2} \sqrt{2 y} + 18 y^{2} \sqrt{2 y}$

Step 2

Simplify by adding terms.

Subtract $6 y^{2} \sqrt{2 y}$ from $y^{2} \sqrt{2 y}$ .

$- 5 y^{2} \sqrt{2 y} + 18 y^{2} \sqrt{2 y}$

Add $- 5 y^{2} \sqrt{2 y}$ and $18 y^{2} \sqrt{2 y}$ .

$13 y^{2} \sqrt{2 y}$

Simplify y square root of 2y^3-3 square root of 8y^5+3y square root of 72y^3

Related Questions

Support LCMGCF.com by disabling your adblocker.