Trigonometry Examples

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

Step 1

Simplify the expression.

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Step 1.1

One to any power is one.

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

Step 1.2

Multiply $- 1$ by $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Rewrite the expression.

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

Step 2.5

Evaluate the exponent.

$\sqrt{- 1 + 2}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $- 1$ and $2$ .

$\sqrt{1}$

Step 3.2

Any root of $1$ is $1$ .

$1$