Solve fx=sqrt{1/2sqrt{1/2sqrt{1/2}}}

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

Solve for f

$$f=\frac{\sqrt[8]{2}}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{\sqrt{1}}{\sqrt{2}}}}$$

Calculate the square root of 1 and get 1.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{1}{\sqrt{2}}}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}}$$

The square of \sqrt{2} is 2.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{\sqrt{2}}{2}}}$$

Multiply \frac{1}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{\sqrt{2}}{2\times 2}}}$$

Multiply 2 and 2 to get 4.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{\sqrt{2}}{4}}}$$

The equation is in standard form.

$$xf=\sqrt{\frac{\sqrt{\frac{\sqrt{2}}{4}}}{2}}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{1}{2^{\frac{7}{8}}x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{1}{2^{\frac{7}{8}}x}$$

Solve for x

$$x=\frac{\sqrt[8]{2}}{2f}$$

$$f\neq 0$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{\sqrt{1}}{\sqrt{2}}}}$$

Calculate the square root of 1 and get 1.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{1}{\sqrt{2}}}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}}$$

The square of \sqrt{2} is 2.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{1}{2}\times \frac{\sqrt{2}}{2}}}$$

Multiply \frac{1}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{\sqrt{2}}{2\times 2}}}$$

Multiply 2 and 2 to get 4.

$$fx=\sqrt{\frac{1}{2}\sqrt{\frac{\sqrt{2}}{4}}}$$

The equation is in standard form.

$$fx=\sqrt{\frac{\sqrt{\frac{\sqrt{2}}{4}}}{2}}$$

Divide both sides by f.

$$\frac{fx}{f}=\frac{1}{2^{\frac{7}{8}}f}$$

Dividing by f undoes the multiplication by f.

$$x=\frac{1}{2^{\frac{7}{8}}f}$$