Solve for n square root of n/5 = square root of 3n-28

$\sqrt{\frac{n}{5}} = \sqrt{3 n - 28}$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{n}{5}}}^{2} = {\sqrt{3 n - 28}}^{2}$

Simplify each side of the equation.

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

${({(\frac{n}{5})}^{\frac{1}{2}})}^{2} = {\sqrt{3 n - 28}}^{2}$

Simplify the left side.

Simplify ${({(\frac{n}{5})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{n}{5})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{n}{5})}^{\frac{1}{2} \cdot 2} = {\sqrt{3 n - 28}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{n}{5})}^{\frac{1}{2} \cdot 2} = {\sqrt{3 n - 28}}^{2}$

Rewrite the expression.

${(\frac{n}{5})}^{1} = {\sqrt{3 n - 28}}^{2}$

Simplify.

$\frac{n}{5} = {\sqrt{3 n - 28}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 n - 28}}^{2}$ as $3 n - 28$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 n - 28}$ as ${(3 n - 28)}^{\frac{1}{2}}$ .

$\frac{n}{5} = {({(3 n - 28)}^{\frac{1}{2}})}^{2}$

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

$\frac{n}{5} = {(3 n - 28)}^{\frac{1}{2} \cdot 2}$

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

$\frac{n}{5} = {(3 n - 28)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{n}{5} = {(3 n - 28)}^{\frac{2}{2}}$

Rewrite the expression.

$\frac{n}{5} = {(3 n - 28)}^{1}$

Simplify.

$\frac{n}{5} = 3 n - 28$

Solve for $n$ .

Multiply both sides by $5$ .

$\frac{n}{5} \cdot 5 = (3 n - 28) \cdot 5$

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{n}{5} \cdot 5 = (3 n - 28) \cdot 5$

Rewrite the expression.

$n = (3 n - 28) \cdot 5$

Simplify the right side.

Simplify $(3 n - 28) \cdot 5$ .

Apply the distributive property.

$n = 3 n \cdot 5 - 28 \cdot 5$

Multiply.

Multiply $5$ by $3$ .

$n = 15 n - 28 \cdot 5$

Multiply $- 28$ by $5$ .

$n = 15 n - 140$

Solve for $n$ .

Move all terms containing $n$ to the left side of the equation.

Subtract $15 n$ from both sides of the equation.

$n - 15 n = - 140$

Subtract $15 n$ from $n$ .

$- 14 n = - 140$

Divide each term in $- 14 n = - 140$ by $- 14$ and simplify.

Divide each term in $- 14 n = - 140$ by $- 14$ .

$\frac{- 14 n}{- 14} = \frac{- 140}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 n}{- 14} = \frac{- 140}{- 14}$

Divide $n$ by $1$ .

$n = \frac{- 140}{- 14}$

Simplify the right side.

Divide $- 140$ by $- 14$ .

$n = 10$

Solve for n square root of n/5 = square root of 3n-28

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