Solve sqrt{3}-sqrt{8}x=sqrt{5-sqrt{24}}

$$\sqrt { 3 } - \sqrt { 8 } x = \sqrt { 5 - \sqrt { 24 } }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\sqrt{3}-2\sqrt{2}x=\sqrt{5-\sqrt{24}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\sqrt{3}-2\sqrt{2}x=\sqrt{5-2\sqrt{6}}$$

Subtract \sqrt{3} from both sides.

$$-2\sqrt{2}x=\sqrt{5-2\sqrt{6}}-\sqrt{3}$$

The equation is in standard form.

$$\left(-2\sqrt{2}\right)x=\sqrt{5-2\sqrt{6}}-\sqrt{3}$$

Divide both sides by -2\sqrt{2}.

$$\frac{\left(-2\sqrt{2}\right)x}{-2\sqrt{2}}=-\frac{\sqrt{2}}{-2\sqrt{2}}$$

Dividing by -2\sqrt{2} undoes the multiplication by -2\sqrt{2}.

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

Divide -\sqrt{2} by -2\sqrt{2}.

$$x=\frac{1}{2}$$