Solve by Factoring square root of x+3=20

$\sqrt{x + 3} = 20$

Step 1

Subtract $20$ from both sides of the equation.

$\sqrt{x + 3} - 20 = 0$

Step 2

Add $20$ to both sides of the equation.

$\sqrt{x + 3} = 20$

Step 3

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

${\sqrt{x + 3}}^{2} = 20^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 3}$ as ${(x + 3)}^{\frac{1}{2}}$ .

${({(x + 3)}^{\frac{1}{2}})}^{2} = 20^{2}$

Simplify the left side.

Simplify ${({(x + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 3)}^{\frac{1}{2}})}^{2}$ .

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

${(x + 3)}^{\frac{1}{2} \cdot 2} = 20^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x + 3)}^{\frac{1}{2} \cdot 2} = 20^{2}$

Rewrite the expression.

${(x + 3)}^{1} = 20^{2}$

Simplify.

$x + 3 = 20^{2}$

Simplify the right side.

Raise $20$ to the power of $2$ .

$x + 3 = 400$

Step 5

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

Subtract $3$ from both sides of the equation.

$x = 400 - 3$

Subtract $3$ from $400$ .

$x = 397$