Finite Math Examples

$\sqrt{40 x^{2} y^{3} z^{8}}$

Step 1

Rewrite $40 x^{2} y^{3} z^{8}$ as ${(2 x y z^{4})}^{2} \cdot (10 y)$ .

Tap for more steps...

Step 1.1

Factor $4$ out of $40$ .

$\sqrt{4 (10) x^{2} y^{3} z^{8}}$

Step 1.2

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

$\sqrt{2^{2} \cdot 10 x^{2} y^{3} z^{8}}$

Step 1.3

Factor out $y^{2}$ .

$\sqrt{2^{2} \cdot 10 x^{2} (y^{2} y) z^{8}}$

Step 1.4

Rewrite $z^{8}$ as ${(z^{4})}^{2}$ .

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

Step 1.5

Move $y$ .

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

Step 1.6

Move $10$ .

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

Step 1.7

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

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

Step 1.8

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$2 x y z^{4} \sqrt{10 y}$