Trigonometry Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.4.1

Cancel the common factor.

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

Step 1.1.4.2

Rewrite the expression.

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

Step 1.1.5

Evaluate the exponent.

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

Step 1.2

Apply the product rule to $- \sqrt{2}$ .

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

Step 1.3

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

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

Step 1.4

Multiply ${\sqrt{2}}^{2}$ by $1$ .

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

Step 1.5

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

Tap for more steps...

Step 1.5.1

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

$v (2 + {(2^{\frac{1}{2}})}^{2})$

Step 1.5.2

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

$v (2 + 2^{\frac{1}{2} \cdot 2})$

Step 1.5.3

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

$v (2 + 2^{\frac{2}{2}})$

Step 1.5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.5.4.1

Cancel the common factor.

$v (2 + 2^{\frac{2}{2}})$

Step 1.5.4.2

Rewrite the expression.

$v (2 + 2^{1})$

Step 1.5.5

Evaluate the exponent.

$v (2 + 2)$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Add $2$ and $2$ .

$v \cdot 4$

Step 2.2

Move $4$ to the left of $v$ .

$4 v$