Basic Math Examples

$12 | m | \sqrt{19} - 6 \sqrt{19 m^{2}} + 8 | m | \sqrt{1216}$

Step 1

Simplify each term.

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Step 1.1

Reorder $19$ and $m^{2}$ .

$12 | m | \sqrt{19} - 6 \sqrt{m^{2} \cdot 19} + 8 | m | \sqrt{1216}$

Step 1.2

Pull terms out from under the radical.

$12 | m | \sqrt{19} - 6 (m \sqrt{19}) + 8 | m | \sqrt{1216}$

Step 1.3

Rewrite $1216$ as $8^{2} \cdot 19$ .

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Step 1.3.1

Factor $64$ out of $1216$ .

$12 | m | \sqrt{19} - 6 m \sqrt{19} + 8 | m | \sqrt{64 (19)}$

Step 1.3.2

Rewrite $64$ as $8^{2}$ .

$12 | m | \sqrt{19} - 6 m \sqrt{19} + 8 | m | \sqrt{8^{2} \cdot 19}$

Step 1.4

Pull terms out from under the radical.

$12 | m | \sqrt{19} - 6 m \sqrt{19} + 8 | m | (8 \sqrt{19})$

Step 1.5

Multiply $8$ by $8$ .

$12 | m | \sqrt{19} - 6 m \sqrt{19} + 64 | m | \sqrt{19}$

Step 2

Add $12 | m | \sqrt{19}$ and $64 | m | \sqrt{19}$ .

$76 | m | \sqrt{19} - 6 m \sqrt{19}$