Algebra Examples

$- {(\sqrt{2})}^{2} - 2 \sqrt{2} + 3$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 1.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- {(2^{\frac{1}{2}})}^{2} - 2 \sqrt{2} + 3$

Step 1.1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 2^{\frac{1}{2} \cdot 2} - 2 \sqrt{2} + 3$

Step 1.1.3

Combine $\frac{1}{2}$ and $2$ .

$- 2^{\frac{2}{2}} - 2 \sqrt{2} + 3$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Cancel the common factor.

$- 2^{\frac{2}{2}} - 2 \sqrt{2} + 3$

Step 1.1.4.2

Rewrite the expression.

$- 2^{1} - 2 \sqrt{2} + 3$

Step 1.1.5

Evaluate the exponent.

$- 1 \cdot 2 - 2 \sqrt{2} + 3$

Step 1.2

Multiply $- 1$ by $2$ .

$- 2 - 2 \sqrt{2} + 3$

Step 2

Add $- 2$ and $3$ .

$1 - 2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$1 - 2 \sqrt{2}$

Decimal Form:

$- 1.82842712 \dots$