Algebra Examples

$(3 \sqrt{32 y}) (4 \sqrt{25 y})$

Step 1

Rewrite $32 y$ as ${(2^{2})}^{2} \cdot (2 y)$ .

Tap for more steps...

Step 1.1

Factor $16$ out of $32$ .

$3 \sqrt{16 (2) y} (4 \sqrt{25 y})$

Step 1.2

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

$3 \sqrt{4^{2} \cdot 2 y} (4 \sqrt{25 y})$

Step 1.3

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

$3 \sqrt{{(2^{2})}^{2} \cdot 2 y} (4 \sqrt{25 y})$

Step 1.4

Add parentheses.

$3 \sqrt{{(2^{2})}^{2} \cdot (2 y)} (4 \sqrt{25 y})$

Step 2

Pull terms out from under the radical.

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

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Raise $2$ to the power of $2$ .

$3 (4 \sqrt{2 y}) (4 \sqrt{25 y})$

Step 3.2

Multiply $4$ by $3$ .

$12 \sqrt{2 y} (4 \sqrt{25 y})$

Step 3.3

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

$12 \sqrt{2 y} (4 \sqrt{5^{2} y})$

Step 4

Pull terms out from under the radical.

$12 \sqrt{2 y} (4 (5 \sqrt{y}))$

Step 5

Multiply $5$ by $4$ .

$12 \sqrt{2 y} (20 \sqrt{y})$

Step 6

Multiply $12 \sqrt{2 y} (20 \sqrt{y})$ .

Tap for more steps...

Step 6.1

Multiply $20$ by $12$ .

$240 \sqrt{2 y} \sqrt{y}$

Step 6.2

Combine using the product rule for radicals.

$240 \sqrt{y (2 y)}$

Step 6.3

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

$240 \sqrt{2 (y^{1} y)}$

Step 6.4

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

$240 \sqrt{2 (y^{1} y^{1})}$

Step 6.5

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

$240 \sqrt{2 y^{1 + 1}}$

Step 6.6

Add $1$ and $1$ .

$240 \sqrt{2 y^{2}}$

Step 7

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

$240 \sqrt{y^{2} \cdot 2}$

Step 8

Pull terms out from under the radical.

$240 y \sqrt{2}$