Simplify the Radical Expression square root of 8y^5* square root of 40y^2

$\sqrt{8 y^{5}} \cdot \sqrt{40 y^{2}}$

Step 1

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

Factor $4$ out of $8$ .

$\sqrt{4 (2) y^{5}} \cdot \sqrt{40 y^{2}}$

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

$\sqrt{2^{2} \cdot 2 y^{5}} \cdot \sqrt{40 y^{2}}$

Factor out $y^{4}$ .

$\sqrt{2^{2} \cdot 2 (y^{4} y)} \cdot \sqrt{40 y^{2}}$

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

$\sqrt{2^{2} \cdot 2 ({(y^{2})}^{2} y)} \cdot \sqrt{40 y^{2}}$

Move $2$ .

$\sqrt{2^{2} {(y^{2})}^{2} \cdot 2 y} \cdot \sqrt{40 y^{2}}$

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

$\sqrt{{(2 y^{2})}^{2} \cdot 2 y} \cdot \sqrt{40 y^{2}}$

Add parentheses.

$\sqrt{{(2 y^{2})}^{2} \cdot (2 y)} \cdot \sqrt{40 y^{2}}$

Step 2

Pull terms out from under the radical.

$| 2 y^{2} | \sqrt{2 y} \cdot \sqrt{40 y^{2}}$

Step 3

Remove non-negative terms from the absolute value.

$2 y^{2} \sqrt{2 y} \cdot \sqrt{40 y^{2}}$

Step 4

Rewrite $40 y^{2}$ as ${(2 y)}^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$2 y^{2} \sqrt{2 y} \cdot \sqrt{4 (10) y^{2}}$

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

$2 y^{2} \sqrt{2 y} \cdot \sqrt{2^{2} \cdot 10 y^{2}}$

Move $10$ .

$2 y^{2} \sqrt{2 y} \cdot \sqrt{2^{2} y^{2} \cdot 10}$

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

$2 y^{2} \sqrt{2 y} \cdot \sqrt{{(2 y)}^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$2 y^{2} \sqrt{2 y} \cdot (| 2 y | \sqrt{10})$

Step 6

Remove non-negative terms from the absolute value.

$2 y^{2} \sqrt{2 y} \cdot (2 | y | \sqrt{10})$

Step 7

Multiply $2 y^{2} \sqrt{2 y} (2 | y | \sqrt{10})$ .

Multiply $2$ by $2$ .

$4 y^{2} \sqrt{2 y} (| y | \sqrt{10})$

Combine using the product rule for radicals.

$4 y^{2} \sqrt{10 (2 y)} | y |$

Multiply $10$ by $2$ .

$4 y^{2} \sqrt{20 y} | y |$

Step 8

Rewrite $20 y$ as $2^{2} \cdot (5 y)$ .

Factor $4$ out of $20$ .

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

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

$4 y^{2} \sqrt{2^{2} \cdot 5 y} | y |$

Add parentheses.

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

Step 9

Pull terms out from under the radical.

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

Step 10

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 11

Multiply $2$ by $4$ .

$8 y^{2} \sqrt{5 y} | y |$

Simplify the Radical Expression square root of 8y^5* square root of 40y^2

Related Questions

Support LCMGCF.com by disabling your adblocker.