Solve for v v^(1/2)+1=0

$v^{\frac{1}{2}} + 1 = 0$

Subtract $1$ from both sides of the equation.

$v^{\frac{1}{2}} = - 1$

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(v^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

Simplify the exponent.

Simplify the left side.

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

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

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

$v^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$v^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Rewrite the expression.

$v^{1} = {(- 1)}^{2}$

Simplify.

$v = {(- 1)}^{2}$

Simplify the right side.

Raise $- 1$ to the power of $2$ .

$v = 1$

Exclude the solutions that do not make $v^{\frac{1}{2}} + 1 = 0$ true.

$No solution$