Basic Math Examples

${(\sqrt{2} - 2)}^{2}$

Step 1

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

$(\sqrt{2} - 2) (\sqrt{2} - 2)$

Step 2

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

Tap for more steps...

Step 2.1

Apply the distributive property.

$\sqrt{2} (\sqrt{2} - 2) - 2 (\sqrt{2} - 2)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Combine using the product rule for radicals.

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

Step 3.1.2

Multiply $2$ by $2$ .

$\sqrt{4} + \sqrt{2} \cdot - 2 - 2 \sqrt{2} - 2 \cdot - 2$

Step 3.1.3

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

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

Step 3.1.4

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

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

Step 3.1.5

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

$2 - 2 \cdot \sqrt{2} - 2 \sqrt{2} - 2 \cdot - 2$

Step 3.1.6

Multiply $- 2$ by $- 2$ .

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

Step 3.2

Add $2$ and $4$ .

$6 - 2 \sqrt{2} - 2 \sqrt{2}$

Step 3.3

Subtract $2 \sqrt{2}$ from $- 2 \sqrt{2}$ .

$6 - 4 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 - 4 \sqrt{2}$

Decimal Form:

$0.34314575 \dots$