Simplify 2 square root of st^2+3 square root of s^2+5 square root of s^3t^4

$2 \sqrt{s t^{2}} + 3 \sqrt{s^{2}} + 5 \sqrt{s^{3} t^{4}}$

Simplify each term.

Reorder $s$ and $t^{2}$ .

$2 \sqrt{t^{2} s} + 3 \sqrt{s^{2}} + 5 \sqrt{s^{3} t^{4}}$

Pull terms out from under the radical.

$2 (t \sqrt{s}) + 3 \sqrt{s^{2}} + 5 \sqrt{s^{3} t^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$2 t \sqrt{s} + 3 s + 5 \sqrt{s^{3} t^{4}}$

Rewrite $s^{3} t^{4}$ as ${(s t^{2})}^{2} s$ .

Factor out $s^{2}$ .

$2 t \sqrt{s} + 3 s + 5 \sqrt{s^{2} s t^{4}}$

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

$2 t \sqrt{s} + 3 s + 5 \sqrt{s^{2} s {(t^{2})}^{2}}$

Move $s$ .

$2 t \sqrt{s} + 3 s + 5 \sqrt{s^{2} {(t^{2})}^{2} s}$

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

$2 t \sqrt{s} + 3 s + 5 \sqrt{{(s t^{2})}^{2} s}$

Pull terms out from under the radical.

$2 t \sqrt{s} + 3 s + 5 s t^{2} \sqrt{s}$

Simplify the expression.

Move $2 t \sqrt{s}$ .

$3 s + 5 s t^{2} \sqrt{s} + 2 t \sqrt{s}$

Reorder $3 s$ and $5 s t^{2} \sqrt{s}$ .

$5 s t^{2} \sqrt{s} + 3 s + 2 t \sqrt{s}$