Solve sqrt{1/3}=frac{sqrt{(T)}}{frac{sqrt{(1)}}{[(1)]}}

$$\sqrt { \frac { 1 } { 3 } } = \frac { \sqrt { ( T ) } } { \frac { \sqrt { ( 1 ) } } { [ ( 1 ) ] } }$$

Solve for T

$$T=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Radical Equations

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\sqrt{1}}{\sqrt{3}}=\frac{\sqrt{T}}{\frac{\sqrt{1}}{1}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{3}}=\frac{\sqrt{T}}{\frac{\sqrt{1}}{1}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=\frac{\sqrt{T}}{\frac{\sqrt{1}}{1}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{3}=\frac{\sqrt{T}}{\frac{\sqrt{1}}{1}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{3}}{3}=\frac{\sqrt{T}}{\frac{1}{1}}$$

Anything divided by one gives itself.

$$\frac{\sqrt{3}}{3}=\frac{\sqrt{T}}{1}$$

Anything divided by one gives itself.

$$\frac{\sqrt{3}}{3}=\sqrt{T}$$

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

$$\sqrt{T}=\frac{\sqrt{3}}{3}$$

Square both sides of the equation.

$$T=\frac{1}{3}$$