Trigonometry Examples

$\frac{45}{\sqrt{0.4}}$

Step 1

Multiply $\frac{45}{\sqrt{0.4}}$ by $\frac{\sqrt{0.4}}{\sqrt{0.4}}$ .

$\frac{45}{\sqrt{0.4}} \cdot \frac{\sqrt{0.4}}{\sqrt{0.4}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{45}{\sqrt{0.4}}$ by $\frac{\sqrt{0.4}}{\sqrt{0.4}}$ .

$\frac{45 \sqrt{0.4}}{\sqrt{0.4} \sqrt{0.4}}$

Step 2.2

Raise $\sqrt{0.4}$ to the power of $1$ .

$\frac{45 \sqrt{0.4}}{{\sqrt{0.4}}^{1} \sqrt{0.4}}$

Step 2.3

Raise $\sqrt{0.4}$ to the power of $1$ .

$\frac{45 \sqrt{0.4}}{{\sqrt{0.4}}^{1} {\sqrt{0.4}}^{1}}$

Step 2.4

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

$\frac{45 \sqrt{0.4}}{{\sqrt{0.4}}^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$\frac{45 \sqrt{0.4}}{{\sqrt{0.4}}^{2}}$

Step 2.6

Rewrite ${\sqrt{0.4}}^{2}$ as $0.4$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.4}$ as ${0.4}^{\frac{1}{2}}$ .

$\frac{45 \sqrt{0.4}}{{({0.4}^{\frac{1}{2}})}^{2}}$

Step 2.6.2

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

$\frac{45 \sqrt{0.4}}{{0.4}^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

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

$\frac{45 \sqrt{0.4}}{{0.4}^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of $2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{45 \sqrt{0.4}}{{0.4}^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{45 \sqrt{0.4}}{{0.4}^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{45 \sqrt{0.4}}{0.4}$

Step 3

Evaluate the root.

$\frac{45 \cdot 0.63245553}{0.4}$

Step 4

Multiply $45$ by $0.63245553$ .

$\frac{28.46049894}{0.4}$

Step 5

Divide $28.46049894$ by $0.4$ .

$71.15124735$