Simplify 2r square root of 49s^5t^10

$2 r \sqrt{49 s^{5} t^{10}}$

Step 1

Rewrite $49 s^{5} t^{10}$ as ${(7 s^{2} t^{5})}^{2} s$ .

Rewrite $49$ as $7^{2}$ .

$2 r \sqrt{7^{2} s^{5} t^{10}}$

Factor out $s^{4}$ .

$2 r \sqrt{7^{2} (s^{4} s) t^{10}}$

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

$2 r \sqrt{7^{2} ({(s^{2})}^{2} s) t^{10}}$

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

$2 r \sqrt{7^{2} ({(s^{2})}^{2} s) {(t^{5})}^{2}}$

Move $s$ .

$2 r \sqrt{7^{2} ({(s^{2})}^{2}) {(t^{5})}^{2} s}$

Rewrite $7^{2} ({(s^{2})}^{2}) {(t^{5})}^{2}$ as ${(7 s^{2} t^{5})}^{2}$ .

$2 r \sqrt{{(7 s^{2} t^{5})}^{2} s}$

Step 2

Pull terms out from under the radical.

$2 r (7 s^{2} t^{5} \sqrt{s})$

Step 3

Multiply $7$ by $2$ .

$14 r s^{2} t^{5} \sqrt{s}$