Trigonometry Examples

$\frac{7}{25} + \frac{9}{\sqrt{145}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Multiply $\frac{9}{\sqrt{145}}$ by $\frac{\sqrt{145}}{\sqrt{145}}$ .

$\frac{7}{25} + \frac{9}{\sqrt{145}} \cdot \frac{\sqrt{145}}{\sqrt{145}}$

Step 1.2

Combine and simplify the denominator.

Tap for more steps...

Step 1.2.1

Multiply $\frac{9}{\sqrt{145}}$ by $\frac{\sqrt{145}}{\sqrt{145}}$ .

$\frac{7}{25} + \frac{9 \sqrt{145}}{\sqrt{145} \sqrt{145}}$

Step 1.2.2

Raise $\sqrt{145}$ to the power of $1$ .

$\frac{7}{25} + \frac{9 \sqrt{145}}{{\sqrt{145}}^{1} \sqrt{145}}$

Step 1.2.3

Raise $\sqrt{145}$ to the power of $1$ .

$\frac{7}{25} + \frac{9 \sqrt{145}}{{\sqrt{145}}^{1} {\sqrt{145}}^{1}}$

Step 1.2.4

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

$\frac{7}{25} + \frac{9 \sqrt{145}}{{\sqrt{145}}^{1 + 1}}$

Step 1.2.5

Add $1$ and $1$ .

$\frac{7}{25} + \frac{9 \sqrt{145}}{{\sqrt{145}}^{2}}$

Step 1.2.6

Rewrite ${\sqrt{145}}^{2}$ as $145$ .

Tap for more steps...

Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{145}$ as $145^{\frac{1}{2}}$ .

$\frac{7}{25} + \frac{9 \sqrt{145}}{{(145^{\frac{1}{2}})}^{2}}$

Step 1.2.6.2

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

$\frac{7}{25} + \frac{9 \sqrt{145}}{145^{\frac{1}{2} \cdot 2}}$

Step 1.2.6.3

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

$\frac{7}{25} + \frac{9 \sqrt{145}}{145^{\frac{2}{2}}}$

Step 1.2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.6.4.1

Cancel the common factor.

$\frac{7}{25} + \frac{9 \sqrt{145}}{145^{\frac{2}{2}}}$

Step 1.2.6.4.2

Rewrite the expression.

$\frac{7}{25} + \frac{9 \sqrt{145}}{145^{1}}$

Step 1.2.6.5

Evaluate the exponent.

$\frac{7}{25} + \frac{9 \sqrt{145}}{145}$

Step 2

To write $\frac{7}{25}$ as a fraction with a common denominator, multiply by $\frac{29}{29}$ .

$\frac{7}{25} \cdot \frac{29}{29} + \frac{9 \sqrt{145}}{145}$

Step 3

To write $\frac{9 \sqrt{145}}{145}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7}{25} \cdot \frac{29}{29} + \frac{9 \sqrt{145}}{145} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $725$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{7}{25}$ by $\frac{29}{29}$ .

$\frac{7 \cdot 29}{25 \cdot 29} + \frac{9 \sqrt{145}}{145} \cdot \frac{5}{5}$

Step 4.2

Multiply $25$ by $29$ .

$\frac{7 \cdot 29}{725} + \frac{9 \sqrt{145}}{145} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{9 \sqrt{145}}{145}$ by $\frac{5}{5}$ .

$\frac{7 \cdot 29}{725} + \frac{9 \sqrt{145} \cdot 5}{145 \cdot 5}$

Step 4.4

Multiply $145$ by $5$ .

$\frac{7 \cdot 29}{725} + \frac{9 \sqrt{145} \cdot 5}{725}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 29 + 9 \sqrt{145} \cdot 5}{725}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $7$ by $29$ .

$\frac{203 + 9 \sqrt{145} \cdot 5}{725}$

Step 6.2

Multiply $5$ by $9$ .

$\frac{203 + 45 \sqrt{145}}{725}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{203 + 45 \sqrt{145}}{725}$

Decimal Form:

$1.02740931 \dots$