Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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Step 1.1.1.1

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

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

Step 1.1.1.2

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

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

Step 1.1.2

Add $1$ and $2$ .

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

Step 1.2

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

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

Step 1.3

Add $2$ and $2$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Multiply $5$ by $2$ .

$f (2) = 8 + 10$

Step 2

Add $8$ and $10$ .

$f (2) = 18$