Solve for n square root of 10-3n=7

$\sqrt{10 - 3 n} = 7$

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

${\sqrt{10 - 3 n}}^{2} = 7^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 - 3 n}$ as ${(10 - 3 n)}^{\frac{1}{2}}$ .

${({(10 - 3 n)}^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

Simplify ${({(10 - 3 n)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(10 - 3 n)}^{\frac{1}{2}})}^{2}$ .

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

${(10 - 3 n)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(10 - 3 n)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(10 - 3 n)}^{1} = 7^{2}$

Simplify.

$10 - 3 n = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$10 - 3 n = 49$

Solve for $n$ .

Move all terms not containing $n$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$- 3 n = 49 - 10$

Subtract $10$ from $49$ .

$- 3 n = 39$

Divide each term in $- 3 n = 39$ by $- 3$ and simplify.

Divide each term in $- 3 n = 39$ by $- 3$ .

$\frac{- 3 n}{- 3} = \frac{39}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 n}{- 3} = \frac{39}{- 3}$

Divide $n$ by $1$ .

$n = \frac{39}{- 3}$

Simplify the right side.

Divide $39$ by $- 3$ .

$n = - 13$