Trigonometry Examples

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

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Apply the product rule to $3 \sqrt{3}$ .

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

Step 1.2

Raise $3$ to the power of $2$ .

$\sqrt{9 {\sqrt{3}}^{2} + 3^{2}}$

Step 2

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

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\sqrt{9 {(3^{\frac{1}{2}})}^{2} + 3^{2}}$

Step 2.2

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

$\sqrt{9 \cdot 3^{\frac{1}{2} \cdot 2} + 3^{2}}$

Step 2.3

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

$\sqrt{9 \cdot 3^{\frac{2}{2}} + 3^{2}}$

Step 2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.1

Cancel the common factor.

$\sqrt{9 \cdot 3^{\frac{2}{2}} + 3^{2}}$

Step 2.4.2

Rewrite the expression.

$\sqrt{9 \cdot 3^{1} + 3^{2}}$

Step 2.5

Evaluate the exponent.

$\sqrt{9 \cdot 3 + 3^{2}}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Multiply $9$ by $3$ .

$\sqrt{27 + 3^{2}}$

Step 3.2

Raise $3$ to the power of $2$ .

$\sqrt{27 + 9}$

Step 3.3

Add $27$ and $9$ .

$\sqrt{36}$

Step 3.4

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}}$

Step 3.5

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

$6$