Solve for a 1+2 = square root of a-1

$1 + 2 = \sqrt{a - 1}$

Step 1

Rewrite the equation as $\sqrt{a - 1} = 1 + 2$ .

$\sqrt{a - 1} = 1 + 2$

Step 2

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

${\sqrt{a - 1}}^{2} = {(1 + 2)}^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(a - 1)}^{1} = {(1 + 2)}^{2}$

Simplify.

$a - 1 = {(1 + 2)}^{2}$

Simplify the right side.

Simplify ${(1 + 2)}^{2}$ .

Add $1$ and $2$ .

$a - 1 = 3^{2}$

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

$a - 1 = 9$

Step 4

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

Add $1$ to both sides of the equation.

$a = 9 + 1$

Add $9$ and $1$ .

$a = 10$