Solve 2=b/sqrt{3/2}

$$2 = \frac { b } { \frac { \sqrt { 3 } } { 2 } }$$

Solve for b

$$b=\sqrt{3}\approx 1.732050808$$

Steps for Solving Linear Equation

Divide b by \frac{\sqrt{3}}{2} by multiplying b by the reciprocal of \frac{\sqrt{3}}{2}.

$$2=\frac{b\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{b\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2=\frac{b\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$2=\frac{b\times 2\sqrt{3}}{3}$$

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

$$\frac{b\times 2\sqrt{3}}{3}=2$$

Multiply both sides by 3.

$$b\times 2\sqrt{3}=2\times 3$$

Cancel out 2 on both sides.

$$b\sqrt{3}=3$$

The equation is in standard form.

$$\sqrt{3}b=3$$

Divide both sides by \sqrt{3}.

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

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

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

Divide 3 by \sqrt{3}.

$$b=\sqrt{3}$$