Solve for v square root of v=-10

$\sqrt{v} = - 10$

Step 1

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

${\sqrt{v}}^{2} = {(- 10)}^{2}$

Step 2

Simplify each side of the equation.

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

${(v^{\frac{1}{2}})}^{2} = {(- 10)}^{2}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$v^{\frac{1}{2} \cdot 2} = {(- 10)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$v^{\frac{1}{2} \cdot 2} = {(- 10)}^{2}$

Rewrite the expression.

$v^{1} = {(- 10)}^{2}$

Simplify.

$v = {(- 10)}^{2}$

Simplify the right side.

Raise $- 10$ to the power of $2$ .

$v = 100$

Step 3

Exclude the solutions that do not make $\sqrt{v} = - 10$ true.

$No solution$