Simplify ( square root of 13f^3)/( square root of 5f^2)

$\frac{\sqrt{13 f^{3}}}{\sqrt{5 f^{2}}}$

Step 1

Combine $\sqrt{13 f^{3}}$ and $\sqrt{5 f^{2}}$ into a single radical.

$\sqrt{\frac{13 f^{3}}{5 f^{2}}}$

Step 2

Reduce the expression $\frac{13 f^{3}}{5 f^{2}}$ by cancelling the common factors.

Factor $f^{2}$ out of $13 f^{3}$ .

$\sqrt{\frac{f^{2} (13 f)}{5 f^{2}}}$

Factor $f^{2}$ out of $5 f^{2}$ .

$\sqrt{\frac{f^{2} (13 f)}{f^{2} \cdot 5}}$

Cancel the common factor.

$\sqrt{\frac{f^{2} (13 f)}{f^{2} \cdot 5}}$

Rewrite the expression.

$\sqrt{\frac{13 f}{5}}$

Step 3

Rewrite $\sqrt{\frac{13 f}{5}}$ as $\frac{\sqrt{13 f}}{\sqrt{5}}$ .

$\frac{\sqrt{13 f}}{\sqrt{5}}$

Step 4

Multiply $\frac{\sqrt{13 f}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt{13 f}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 5

Combine and simplify the denominator.

Multiply $\frac{\sqrt{13 f}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{\sqrt{13 f} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\sqrt{13 f} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{\sqrt{13 f} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

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

$\frac{\sqrt{13 f} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{13 f} \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{\sqrt{13 f} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{13 f} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{13 f} \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{13 f} \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{13 f} \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$\frac{\sqrt{13 f} \sqrt{5}}{5}$

Step 6

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{13 f \cdot 5}}{5}$

Multiply $5$ by $13$ .

$\frac{\sqrt{65 f}}{5}$

Simplify ( square root of 13f^3)/( square root of 5f^2)

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