Solve for m square root of 2m+3=n

$\sqrt{2 m + 3} = n$

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

${\sqrt{2 m + 3}}^{2} = n^{2}$

Simplify each side of the equation.

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

${({(2 m + 3)}^{\frac{1}{2}})}^{2} = n^{2}$

Simplify the left side.

Simplify ${({(2 m + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 m + 3)}^{\frac{1}{2}})}^{2}$ .

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

${(2 m + 3)}^{\frac{1}{2} \cdot 2} = n^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 m + 3)}^{\frac{1}{2} \cdot 2} = n^{2}$

Rewrite the expression.

${(2 m + 3)}^{1} = n^{2}$

Simplify.

$2 m + 3 = n^{2}$

Solve for $m$ .

Subtract $3$ from both sides of the equation.

$2 m = n^{2} - 3$

Divide each term in $2 m = n^{2} - 3$ by $2$ and simplify.

Divide each term in $2 m = n^{2} - 3$ by $2$ .

$\frac{2 m}{2} = \frac{n^{2}}{2} + \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 m}{2} = \frac{n^{2}}{2} + \frac{- 3}{2}$

Divide $m$ by $1$ .

$m = \frac{n^{2}}{2} + \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$m = \frac{n^{2}}{2} - \frac{3}{2}$