Basic Math Examples

$7 y \sqrt{50 y} - 4 \sqrt{18 y^{3}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $50 y$ as $5^{2} \cdot (2 y)$ .

Tap for more steps...

Step 1.1.1

Factor $25$ out of $50$ .

$7 y \sqrt{25 (2) y} - 4 \sqrt{18 y^{3}}$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

$7 y \sqrt{5^{2} \cdot 2 y} - 4 \sqrt{18 y^{3}}$

Step 1.1.3

Add parentheses.

$7 y \sqrt{5^{2} \cdot (2 y)} - 4 \sqrt{18 y^{3}}$

Step 1.2

Pull terms out from under the radical.

$7 y (5 \sqrt{2 y}) - 4 \sqrt{18 y^{3}}$

Step 1.3

Multiply $5$ by $7$ .

$35 y \sqrt{2 y} - 4 \sqrt{18 y^{3}}$

Step 1.4

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

Tap for more steps...

Step 1.4.1

Factor $9$ out of $18$ .

$35 y \sqrt{2 y} - 4 \sqrt{9 (2) y^{3}}$

Step 1.4.2

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

$35 y \sqrt{2 y} - 4 \sqrt{3^{2} \cdot 2 y^{3}}$

Step 1.4.3

Factor out $y^{2}$ .

$35 y \sqrt{2 y} - 4 \sqrt{3^{2} \cdot 2 (y^{2} y)}$

Step 1.4.4

Move $2$ .

$35 y \sqrt{2 y} - 4 \sqrt{3^{2} y^{2} \cdot 2 y}$

Step 1.4.5

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

$35 y \sqrt{2 y} - 4 \sqrt{{(3 y)}^{2} \cdot 2 y}$

Step 1.4.6

Add parentheses.

$35 y \sqrt{2 y} - 4 \sqrt{{(3 y)}^{2} \cdot (2 y)}$

Step 1.5

Pull terms out from under the radical.

$35 y \sqrt{2 y} - 4 (3 y \sqrt{2 y})$

Step 1.6

Multiply $3$ by $- 4$ .

$35 y \sqrt{2 y} - 12 y \sqrt{2 y}$

Step 2

Subtract $12 y \sqrt{2 y}$ from $35 y \sqrt{2 y}$ .

$23 y \sqrt{2 y}$