Solve 2sqrt{180}-frac{sqrt{180}}{2}=sqrt{x}

$$2 \sqrt{ 180 } - \frac{ \sqrt{ 180 } }{ 2 } = \sqrt{ x }$$

Solve for x

$$x=405$$

Steps for Solving Radical Equations

Multiply both sides of the equation by 2.

$$4\sqrt{180}-\sqrt{180}=2\sqrt{x}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$4\times 6\sqrt{5}-\sqrt{180}=2\sqrt{x}$$

Multiply 4 and 6 to get 24.

$$24\sqrt{5}-\sqrt{180}=2\sqrt{x}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$24\sqrt{5}-6\sqrt{5}=2\sqrt{x}$$

Swap sides so that all variable terms are on the left hand side.

$$2\sqrt{x}=24\sqrt{5}-6\sqrt{5}$$

Combine 24\sqrt{5} and -6\sqrt{5} to get 18\sqrt{5}.

$$2\sqrt{x}=18\sqrt{5}$$

Divide both sides by 2.

$$\frac{2\sqrt{x}}{2}=\frac{18\sqrt{5}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{x}=\frac{18\sqrt{5}}{2}$$

Divide 18\sqrt{5} by 2.

$$\sqrt{x}=9\sqrt{5}$$

Square both sides of the equation.

$$x=405$$