Evaluate Using the Given Value f(12) = square root of 3(12)+12

$f (12) = \sqrt{3 (12) + 12}$

Step 1

Multiply $3$ by $12$ .

$f (12) = \sqrt{36 + 12}$

Step 2

Add $36$ and $12$ .

$f (12) = \sqrt{48}$

Step 3

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$f (12) = \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$f (12) = \sqrt{4^{2} \cdot 3}$

Step 4

Pull terms out from under the radical.

$f (12) = 4 \sqrt{3}$