Solve for x y = square root of x+a

$y = \sqrt{x + a}$

Step 1

Rewrite the equation as $\sqrt{x + a} = y$ .

$\sqrt{x + a} = y$

Step 2

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

${\sqrt{x + a}}^{2} = y^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(x + a)}^{1} = y^{2}$

Simplify.

$x + a = y^{2}$

Step 4

Subtract $a$ from both sides of the equation.

$x = y^{2} - a$