Evaluate Using the Given Value f(2)=2(2)^2+5 square root of 2+2

$f (2) = 2 {(2)}^{2} + 5 \sqrt{2 + 2}$

Step 1

Simplify each term.

Multiply $2$ by ${(2)}^{2}$ by adding the exponents.

Multiply $2$ by ${(2)}^{2}$ .

Raise $2$ to the power of $1$ .

$f (2) = 2 {(2)}^{2} + 5 \sqrt{2 + 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 2^{1 + 2} + 5 \sqrt{2 + 2}$

Add $1$ and $2$ .

$f (2) = 2^{3} + 5 \sqrt{2 + 2}$

Raise $2$ to the power of $3$ .

$f (2) = 8 + 5 \sqrt{2 + 2}$

Add $2$ and $2$ .

$f (2) = 8 + 5 \sqrt{4}$

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

$f (2) = 8 + 5 \sqrt{2^{2}}$

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

$f (2) = 8 + 5 \cdot 2$

Multiply $5$ by $2$ .

$f (2) = 8 + 10$

Step 2

Add $8$ and $10$ .

$f (2) = 18$