Solve for x 4=1+ square root of x

$4 = 1 + \sqrt{x}$

Step 1

Rewrite the equation as $1 + \sqrt{x} = 4$ .

$1 + \sqrt{x} = 4$

Step 2

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

Subtract $1$ from both sides of the equation.

$\sqrt{x} = 4 - 1$

Subtract $1$ from $4$ .

$\sqrt{x} = 3$

Step 3

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

${\sqrt{x}}^{2} = 3^{2}$

Step 4

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

$x^{1} = 3^{2}$

Simplify.

$x = 3^{2}$

Simplify the right side.

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

$x = 9$