Solve for b square root of b-2=10

$\sqrt{b} - 2 = 10$

Step 1

Move all terms not containing $\sqrt{b}$ to the right side of the equation.

Add $2$ to both sides of the equation.

$\sqrt{b} = 10 + 2$

Add $10$ and $2$ .

$\sqrt{b} = 12$

Step 2

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

${\sqrt{b}}^{2} = 12^{2}$

Step 3

Simplify each side of the equation.

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

${(b^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

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

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

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

$b^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$b^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$b^{1} = 12^{2}$

Simplify.

$b = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$b = 144$