Trigonometry Examples

v ({(12)}^{2} + {(4 \sqrt{3})}^{2})

$v ({(12)}^{2} + {(4 \sqrt{3})}^{2})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Raise

12

$12$ to the power of

2

$2$ .

v (144 + {(4 \sqrt{3})}^{2})

$v (144 + {(4 \sqrt{3})}^{2})$

Step 1.2

Apply the product rule to

4 \sqrt{3}

$4 \sqrt{3}$ .

v (144 + 4^{2} {\sqrt{3}}^{2})

$v (144 + 4^{2} {\sqrt{3}}^{2})$

Step 1.3

Raise

4

$4$ to the power of

2

$2$ .

v (144 + 16 {\sqrt{3}}^{2})

$v (144 + 16 {\sqrt{3}}^{2})$

Step 1.4

Rewrite

{\sqrt{3}}^{2}

${\sqrt{3}}^{2}$ as

3

$3$ .

Tap for more steps...

Step 1.4.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{3}

$\sqrt{3}$ as

3^{\frac{1}{2}}

$3^{\frac{1}{2}}$ .

v (144 + 16 {(3^{\frac{1}{2}})}^{2})

$v (144 + 16 {(3^{\frac{1}{2}})}^{2})$

Step 1.4.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

v (144 + 16 \cdot 3^{\frac{1}{2} \cdot 2})

$v (144 + 16 \cdot 3^{\frac{1}{2} \cdot 2})$

Step 1.4.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

v (144 + 16 \cdot 3^{\frac{2}{2}})

$v (144 + 16 \cdot 3^{\frac{2}{2}})$

Step 1.4.4

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 1.4.4.1

Cancel the common factor.

v (144 + 16 \cdot 3^{\frac{2}{2}})

$v (144 + 16 \cdot 3^{\frac{2}{2}})$

Step 1.4.4.2

Rewrite the expression.

v (144 + 16 \cdot 3^{1})

$v (144 + 16 \cdot 3^{1})$

v (144 + 16 \cdot 3^{1})

$v (144 + 16 \cdot 3^{1})$

Step 1.4.5

Evaluate the exponent.

v (144 + 16 \cdot 3)

$v (144 + 16 \cdot 3)$

v (144 + 16 \cdot 3)

$v (144 + 16 \cdot 3)$

Step 1.5

Multiply

16

$16$ by

3

$3$ .

v (144 + 48)

$v (144 + 48)$

v (144 + 48)

$v (144 + 48)$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Add

144

$144$ and

48

$48$ .

v \cdot 192

$v \cdot 192$

Step 2.2

Move

192

$192$ to the left of

v

$v$ .

192 v

$192 v$

192 v

$192 v$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$