Finite Math Examples

$\sqrt{50 t^{7} w^{11}}$

Step 1

Rewrite $50 t^{7} w^{11}$ as ${(5 t^{3} w^{5})}^{2} \cdot (2 t w)$ .

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Step 1.1

Factor $25$ out of $50$ .

$\sqrt{25 (2) t^{7} w^{11}}$

Step 1.2

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

$\sqrt{5^{2} \cdot 2 t^{7} w^{11}}$

Step 1.3

Factor out $t^{6}$ .

$\sqrt{5^{2} \cdot 2 (t^{6} t) w^{11}}$

Step 1.4

Rewrite $t^{6}$ as ${(t^{3})}^{2}$ .

$\sqrt{5^{2} \cdot 2 ({(t^{3})}^{2} t) w^{11}}$

Step 1.5

Factor out $w^{10}$ .

$\sqrt{5^{2} \cdot 2 ({(t^{3})}^{2} t) (w^{10} w)}$

Step 1.6

Rewrite $w^{10}$ as ${(w^{5})}^{2}$ .

$\sqrt{5^{2} \cdot 2 ({(t^{3})}^{2} t) ({(w^{5})}^{2} w)}$

Step 1.7

Move $t$ .

$\sqrt{5^{2} \cdot 2 ({(t^{3})}^{2}) {(w^{5})}^{2} t w}$

Step 1.8

Move $2$ .

$\sqrt{(5^{2} ({(t^{3})}^{2})) {(w^{5})}^{2} \cdot 2 t w}$

Step 1.9

Rewrite $(5^{2} ({(t^{3})}^{2})) {(w^{5})}^{2}$ as ${(5 t^{3} w^{5})}^{2}$ .

$\sqrt{{(5 t^{3} w^{5})}^{2} \cdot 2 t w}$

Step 1.10

Add parentheses.

$\sqrt{{(5 t^{3} w^{5})}^{2} \cdot 2 (t w)}$

Step 1.11

Add parentheses.

$\sqrt{{(5 t^{3} w^{5})}^{2} \cdot (2 t w)}$

Step 2

Pull terms out from under the radical.

$5 t^{3} w^{5} \sqrt{2 t w}$