Basic Math Examples

$9 \sqrt{\frac{2}{13}} - \frac{7}{\sqrt{26}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $\sqrt{\frac{2}{13}}$ as $\frac{\sqrt{2}}{\sqrt{13}}$ .

$9 \frac{\sqrt{2}}{\sqrt{13}} - \frac{7}{\sqrt{26}}$

Step 1.2

Multiply $\frac{\sqrt{2}}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$9 (\frac{\sqrt{2}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}) - \frac{7}{\sqrt{26}}$

Step 1.3

Combine and simplify the denominator.

Tap for more steps...

Step 1.3.1

Multiply $\frac{\sqrt{2}}{\sqrt{13}}$ by $\frac{\sqrt{13}}{\sqrt{13}}$ .

$9 \frac{\sqrt{2} \sqrt{13}}{\sqrt{13} \sqrt{13}} - \frac{7}{\sqrt{26}}$

Step 1.3.2

Raise $\sqrt{13}$ to the power of $1$ .

$9 \frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{1} \sqrt{13}} - \frac{7}{\sqrt{26}}$

Step 1.3.3

Raise $\sqrt{13}$ to the power of $1$ .

$9 \frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{1} {\sqrt{13}}^{1}} - \frac{7}{\sqrt{26}}$

Step 1.3.4

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

$9 \frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{1 + 1}} - \frac{7}{\sqrt{26}}$

Step 1.3.5

Add $1$ and $1$ .

$9 \frac{\sqrt{2} \sqrt{13}}{{\sqrt{13}}^{2}} - \frac{7}{\sqrt{26}}$

Step 1.3.6

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Tap for more steps...

Step 1.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$9 \frac{\sqrt{2} \sqrt{13}}{{(13^{\frac{1}{2}})}^{2}} - \frac{7}{\sqrt{26}}$

Step 1.3.6.2

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

$9 \frac{\sqrt{2} \sqrt{13}}{13^{\frac{1}{2} \cdot 2}} - \frac{7}{\sqrt{26}}$

Step 1.3.6.3

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

$9 \frac{\sqrt{2} \sqrt{13}}{13^{\frac{2}{2}}} - \frac{7}{\sqrt{26}}$

Step 1.3.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.6.4.1

Cancel the common factor.

$9 \frac{\sqrt{2} \sqrt{13}}{13^{\frac{2}{2}}} - \frac{7}{\sqrt{26}}$

Step 1.3.6.4.2

Rewrite the expression.

$9 \frac{\sqrt{2} \sqrt{13}}{13^{1}} - \frac{7}{\sqrt{26}}$

Step 1.3.6.5

Evaluate the exponent.

$9 \frac{\sqrt{2} \sqrt{13}}{13} - \frac{7}{\sqrt{26}}$

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Combine using the product rule for radicals.

$9 \frac{\sqrt{2 \cdot 13}}{13} - \frac{7}{\sqrt{26}}$

Step 1.4.2

Multiply $2$ by $13$ .

$9 \frac{\sqrt{26}}{13} - \frac{7}{\sqrt{26}}$

Step 1.5

Combine $9$ and $\frac{\sqrt{26}}{13}$ .

$\frac{9 \sqrt{26}}{13} - \frac{7}{\sqrt{26}}$

Step 1.6

Multiply $\frac{7}{\sqrt{26}}$ by $\frac{\sqrt{26}}{\sqrt{26}}$ .

$\frac{9 \sqrt{26}}{13} - (\frac{7}{\sqrt{26}} \cdot \frac{\sqrt{26}}{\sqrt{26}})$

Step 1.7

Combine and simplify the denominator.

Tap for more steps...

Step 1.7.1

Multiply $\frac{7}{\sqrt{26}}$ by $\frac{\sqrt{26}}{\sqrt{26}}$ .

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{\sqrt{26} \sqrt{26}}$

Step 1.7.2

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{{\sqrt{26}}^{1} \sqrt{26}}$

Step 1.7.3

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{{\sqrt{26}}^{1} {\sqrt{26}}^{1}}$

Step 1.7.4

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

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{{\sqrt{26}}^{1 + 1}}$

Step 1.7.5

Add $1$ and $1$ .

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{{\sqrt{26}}^{2}}$

Step 1.7.6

Rewrite ${\sqrt{26}}^{2}$ as $26$ .

Tap for more steps...

Step 1.7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{26}$ as $26^{\frac{1}{2}}$ .

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{{(26^{\frac{1}{2}})}^{2}}$

Step 1.7.6.2

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

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{26^{\frac{1}{2} \cdot 2}}$

Step 1.7.6.3

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

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{26^{\frac{2}{2}}}$

Step 1.7.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.7.6.4.1

Cancel the common factor.

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{26^{\frac{2}{2}}}$

Step 1.7.6.4.2

Rewrite the expression.

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{26^{1}}$

Step 1.7.6.5

Evaluate the exponent.

$\frac{9 \sqrt{26}}{13} - \frac{7 \sqrt{26}}{26}$

Step 2

To write $\frac{9 \sqrt{26}}{13}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 \sqrt{26}}{13} \cdot \frac{2}{2} - \frac{7 \sqrt{26}}{26}$

Step 3

Write each expression with a common denominator of $26$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{9 \sqrt{26}}{13}$ by $\frac{2}{2}$ .

$\frac{9 \sqrt{26} \cdot 2}{13 \cdot 2} - \frac{7 \sqrt{26}}{26}$

Step 3.2

Multiply $13$ by $2$ .

$\frac{9 \sqrt{26} \cdot 2}{26} - \frac{7 \sqrt{26}}{26}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \sqrt{26} \cdot 2 - 7 \sqrt{26}}{26}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $2$ by $9$ .

$\frac{18 \sqrt{26} - 7 \sqrt{26}}{26}$

Step 5.2

Subtract $7 \sqrt{26}$ from $18 \sqrt{26}$ .

$\frac{11 \sqrt{26}}{26}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{11 \sqrt{26}}{26}$

Decimal Form:

$2.15727748 \dots$