Pre-Algebra Examples

${(\sqrt{7} + 2)}^{2}$

Step 1

Rewrite ${(\sqrt{7} + 2)}^{2}$ as $(\sqrt{7} + 2) (\sqrt{7} + 2)$ .

$(\sqrt{7} + 2) (\sqrt{7} + 2)$

Step 2

Expand $(\sqrt{7} + 2) (\sqrt{7} + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\sqrt{7} (\sqrt{7} + 2) + 2 (\sqrt{7} + 2)$

Step 2.2

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} \cdot 2 + 2 (\sqrt{7} + 2)$

Step 2.3

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} \cdot 2 + 2 \sqrt{7} + 2 \cdot 2$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Combine using the product rule for radicals.

$\sqrt{7 \cdot 7} + \sqrt{7} \cdot 2 + 2 \sqrt{7} + 2 \cdot 2$

Step 3.1.2

Multiply $7$ by $7$ .

$\sqrt{49} + \sqrt{7} \cdot 2 + 2 \sqrt{7} + 2 \cdot 2$

Step 3.1.3

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}} + \sqrt{7} \cdot 2 + 2 \sqrt{7} + 2 \cdot 2$

Step 3.1.4

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

$7 + \sqrt{7} \cdot 2 + 2 \sqrt{7} + 2 \cdot 2$

Step 3.1.5

Move $2$ to the left of $\sqrt{7}$ .

$7 + 2 \cdot \sqrt{7} + 2 \sqrt{7} + 2 \cdot 2$

Step 3.1.6

Multiply $2$ by $2$ .

$7 + 2 \sqrt{7} + 2 \sqrt{7} + 4$

Step 3.2

Add $7$ and $4$ .

$11 + 2 \sqrt{7} + 2 \sqrt{7}$

Step 3.3

Add $2 \sqrt{7}$ and $2 \sqrt{7}$ .

$11 + 4 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$11 + 4 \sqrt{7}$

Decimal Form:

$21.58300524 \dots$