Trigonometry Examples

$1.64 \cdot \frac{213}{\sqrt{71}}$

Step 1

Multiply $\frac{213}{\sqrt{71}}$ by $\frac{\sqrt{71}}{\sqrt{71}}$ .

$1.64 \cdot (\frac{213}{\sqrt{71}} \cdot \frac{\sqrt{71}}{\sqrt{71}})$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{213}{\sqrt{71}}$ by $\frac{\sqrt{71}}{\sqrt{71}}$ .

$1.64 \cdot \frac{213 \sqrt{71}}{\sqrt{71} \sqrt{71}}$

Step 2.2

Raise $\sqrt{71}$ to the power of $1$ .

$1.64 \cdot \frac{213 \sqrt{71}}{{\sqrt{71}}^{1} \sqrt{71}}$

Step 2.3

Raise $\sqrt{71}$ to the power of $1$ .

$1.64 \cdot \frac{213 \sqrt{71}}{{\sqrt{71}}^{1} {\sqrt{71}}^{1}}$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1.64 \cdot \frac{213 \sqrt{71}}{{\sqrt{71}}^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$1.64 \cdot \frac{213 \sqrt{71}}{{\sqrt{71}}^{2}}$

Step 2.6

Rewrite ${\sqrt{71}}^{2}$ as $71$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{71}$ as $71^{\frac{1}{2}}$ .

$1.64 \cdot \frac{213 \sqrt{71}}{{(71^{\frac{1}{2}})}^{2}}$

Step 2.6.2

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

$1.64 \cdot \frac{213 \sqrt{71}}{71^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

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

$1.64 \cdot \frac{213 \sqrt{71}}{71^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$1.64 \cdot \frac{213 \sqrt{71}}{71^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$1.64 \cdot \frac{213 \sqrt{71}}{71^{1}}$

Step 2.6.5

Evaluate the exponent.

$1.64 \cdot \frac{213 \sqrt{71}}{71}$

Step 3

Cancel the common factor of $213$ and $71$ .

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Step 3.1

Factor $71$ out of $213 \sqrt{71}$ .

$1.64 \cdot \frac{71 (3 \sqrt{71})}{71}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $71$ out of $71$ .

$1.64 \cdot \frac{71 (3 \sqrt{71})}{71 (1)}$

Step 3.2.2

Cancel the common factor.

$1.64 \cdot \frac{71 (3 \sqrt{71})}{71 \cdot 1}$

Step 3.2.3

Rewrite the expression.

$1.64 \cdot \frac{3 \sqrt{71}}{1}$

Step 3.2.4

Divide $3 \sqrt{71}$ by $1$ .

$1.64 \cdot (3 \sqrt{71})$

Step 4

Multiply $1.64 (3 \sqrt{71})$ .

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Step 4.1

Multiply $3$ by $1.64$ .

$4.92 \sqrt{71}$

Step 4.2

Multiply $4.92$ by $\sqrt{71}$ .

$41.45665688$