Solve the Rational Equation for b -5 square root of b=-50

$- 5 \sqrt{b} = - 50$

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

${(- 5 \sqrt{b})}^{2} = {(- 50)}^{2}$

Simplify each side of the equation.

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

${(- 5 b^{\frac{1}{2}})}^{2} = {(- 50)}^{2}$

Simplify the left side.

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

Apply the product rule to $- 5 b^{\frac{1}{2}}$ .

${(- 5)}^{2} {(b^{\frac{1}{2}})}^{2} = {(- 50)}^{2}$

Raise $- 5$ to the power of $2$ .

$25 {(b^{\frac{1}{2}})}^{2} = {(- 50)}^{2}$

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

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

$25 b^{\frac{1}{2} \cdot 2} = {(- 50)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 b^{\frac{1}{2} \cdot 2} = {(- 50)}^{2}$

Rewrite the expression.

$25 b^{1} = {(- 50)}^{2}$

Simplify.

$25 b = {(- 50)}^{2}$

Simplify the right side.

Raise $- 50$ to the power of $2$ .

$25 b = 2500$

Divide each term in $25 b = 2500$ by $25$ and simplify.

Divide each term in $25 b = 2500$ by $25$ .

$\frac{25 b}{25} = \frac{2500}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 b}{25} = \frac{2500}{25}$

Divide $b$ by $1$ .

$b = \frac{2500}{25}$

Simplify the right side.

Divide $2500$ by $25$ .

$b = 100$