Simplify the Radical Expression ( square root of 5n)/(2 square root of 15n^4)

$\frac{\sqrt{5 n}}{2 \sqrt{15 n^{4}}}$

Combine $\sqrt{5 n}$ and $\sqrt{15 n^{4}}$ into a single radical.

$\frac{\sqrt{\frac{5 n}{15 n^{4}}}}{2}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5 n$ .

$\frac{\sqrt{\frac{5 (n)}{15 n^{4}}}}{2}$

Cancel the common factors.

Factor $5$ out of $15 n^{4}$ .

$\frac{\sqrt{\frac{5 (n)}{5 (3 n^{4})}}}{2}$

Cancel the common factor.

$\frac{\sqrt{\frac{5 n}{5 (3 n^{4})}}}{2}$

Rewrite the expression.

$\frac{\sqrt{\frac{n}{3 n^{4}}}}{2}$

Cancel the common factor of $n$ and $n^{4}$ .

Raise $n$ to the power of $1$ .

$\frac{\sqrt{\frac{n^{1}}{3 n^{4}}}}{2}$

Factor $n$ out of $n^{1}$ .

$\frac{\sqrt{\frac{n \cdot 1}{3 n^{4}}}}{2}$

Cancel the common factors.

Factor $n$ out of $3 n^{4}$ .

$\frac{\sqrt{\frac{n \cdot 1}{n (3 n^{3})}}}{2}$

Cancel the common factor.

$\frac{\sqrt{\frac{n \cdot 1}{n (3 n^{3})}}}{2}$

Rewrite the expression.

$\frac{\sqrt{\frac{1}{3 n^{3}}}}{2}$

Simplify the numerator.

Rewrite $\frac{1}{3 n^{3}}$ as ${(\frac{1}{n})}^{2} \frac{1}{3 n}$ .

Factor the perfect power $1^{2}$ out of $1$ .

$\frac{\sqrt{\frac{1^{2} \cdot 1}{3 n^{3}}}}{2}$

Factor the perfect power $n^{2}$ out of $3 n^{3}$ .

$\frac{\sqrt{\frac{1^{2} \cdot 1}{n^{2} \cdot (3 n)}}}{2}$

Rearrange the fraction $\frac{1^{2} \cdot 1}{n^{2} \cdot (3 n)}$ .

$\frac{\sqrt{{(\frac{1}{n})}^{2} \frac{1}{3 n}}}{2}$

Pull terms out from under the radical.

$\frac{| \frac{1}{n} | \sqrt{\frac{1}{3 n}}}{2}$

Rewrite $\sqrt{\frac{1}{3 n}}$ as $\frac{\sqrt{1}}{\sqrt{3 n}}$ .

$\frac{| \frac{1}{n} | \frac{\sqrt{1}}{\sqrt{3 n}}}{2}$

Any root of $1$ is $1$ .

$\frac{| \frac{1}{n} | \frac{1}{\sqrt{3 n}}}{2}$

Multiply $\frac{1}{\sqrt{3 n}}$ by $\frac{\sqrt{3 n}}{\sqrt{3 n}}$ .

$\frac{| \frac{1}{n} | (\frac{1}{\sqrt{3 n}} \cdot \frac{\sqrt{3 n}}{\sqrt{3 n}})}{2}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{3 n}}$ by $\frac{\sqrt{3 n}}{\sqrt{3 n}}$ .

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{\sqrt{3 n} \sqrt{3 n}}}{2}$

Raise $\sqrt{3 n}$ to the power of $1$ .

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{\sqrt{3 n}}^{1} \sqrt{3 n}}}{2}$

Raise $\sqrt{3 n}$ to the power of $1$ .

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{\sqrt{3 n}}^{1} {\sqrt{3 n}}^{1}}}{2}$

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

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{\sqrt{3 n}}^{1 + 1}}}{2}$

Add $1$ and $1$ .

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{\sqrt{3 n}}^{2}}}{2}$

Rewrite ${\sqrt{3 n}}^{2}$ as $3 n$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 n}$ as ${(3 n)}^{\frac{1}{2}}$ .

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{({(3 n)}^{\frac{1}{2}})}^{2}}}{2}$

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

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{(3 n)}^{\frac{1}{2} \cdot 2}}}{2}$

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

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{(3 n)}^{\frac{2}{2}}}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{(3 n)}^{\frac{2}{2}}}}{2}$

Rewrite the expression.

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{{(3 n)}^{1}}}{2}$

Simplify.

$\frac{| \frac{1}{n} | \frac{\sqrt{3 n}}{3 n}}{2}$

Combine $| \frac{1}{n} |$ and $\frac{\sqrt{3 n}}{3 n}$ .

$\frac{\frac{| \frac{1}{n} | \sqrt{3 n}}{3 n}}{2}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{| \frac{1}{n} | \sqrt{3 n}}{3 n} \cdot \frac{1}{2}$

Multiply $\frac{| \frac{1}{n} | \sqrt{3 n}}{3 n} \cdot \frac{1}{2}$ .

Multiply $\frac{| \frac{1}{n} | \sqrt{3 n}}{3 n}$ by $\frac{1}{2}$ .

$\frac{| \frac{1}{n} | \sqrt{3 n}}{3 n \cdot 2}$

Multiply $2$ by $3$ .

$\frac{| \frac{1}{n} | \sqrt{3 n}}{6 n}$

Simplify the Radical Expression ( square root of 5n)/(2 square root of 15n^4)

Related Questions

Support LCMGCF.com by disabling your adblocker.