Algebra Examples

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

Step 1

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Pull terms out from under the radical.

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

Step 4

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

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Step 4.1

Factor out $s^{2}$ .

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

Step 4.2

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

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

Step 4.3

Move $s$ .

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

Step 4.4

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Remove non-negative terms from the absolute value.

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