Solve by Factoring 3 = square root of b-1

$3 = \sqrt{b - 1}$

Step 1

Subtract $\sqrt{b - 1}$ from both sides of the equation.

$3 - \sqrt{b - 1} = 0$

Step 2

Subtract $3$ from both sides of the equation.

$- \sqrt{b - 1} = - 3$

Step 3

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

${(- \sqrt{b - 1})}^{2} = {(- 3)}^{2}$

Step 4

Simplify each side of the equation.

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

${(- {(b - 1)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Simplify the left side.

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

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

${(- 1)}^{2} {({(b - 1)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

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

$1 {({(b - 1)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Multiply ${({(b - 1)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(b - 1)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

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

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

${(b - 1)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(b - 1)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Rewrite the expression.

${(b - 1)}^{1} = {(- 3)}^{2}$

Simplify.

$b - 1 = {(- 3)}^{2}$

Simplify the right side.

Raise $- 3$ to the power of $2$ .

$b - 1 = 9$

Step 5

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

Add $1$ to both sides of the equation.

$b = 9 + 1$

Add $9$ and $1$ .

$b = 10$