Solve A=sqrt{3+2sqrt{2}-sqrt{3-2sqrt{2}}}quadB

$$A = \sqrt { 3 + 2 \sqrt { 2 } - \sqrt { 3 - 2 \sqrt { 2 } } } \quad B$$

Solve for B

$$B=\frac{\sqrt{56-14\sqrt{2}}A}{14}$$

Steps for Solving Linear Equation

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

$$\sqrt{3+2\sqrt{2}-\sqrt{3-2\sqrt{2}}}B=A$$

The equation is in standard form.

$$\sqrt{-\sqrt{3-2\sqrt{2}}+2\sqrt{2}+3}B=A$$

Divide both sides by \sqrt{3+2\sqrt{2}-\sqrt{3-2\sqrt{2}}}.

$$\frac{\sqrt{-\sqrt{3-2\sqrt{2}}+2\sqrt{2}+3}B}{\sqrt{-\sqrt{3-2\sqrt{2}}+2\sqrt{2}+3}}=\frac{A}{\sqrt{-\sqrt{3-2\sqrt{2}}+2\sqrt{2}+3}}$$

Dividing by \sqrt{3+2\sqrt{2}-\sqrt{3-2\sqrt{2}}} undoes the multiplication by \sqrt{3+2\sqrt{2}-\sqrt{3-2\sqrt{2}}}.

$$B=\frac{A}{\sqrt{-\sqrt{3-2\sqrt{2}}+2\sqrt{2}+3}}$$

Divide A by \sqrt{3+2\sqrt{2}-\sqrt{3-2\sqrt{2}}}.

$$B=\frac{\sqrt{56-14\sqrt{2}}A}{14}$$

Solve for A

$$A=\sqrt{\sqrt{2}+4}B$$