1. **State the problem:** Calculate the value of $\left(\frac{\sqrt{3}}{2}\right)^2$. 2. **Formula used:** When squaring a fraction, square the numerator and the denominator separately: $$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$ 3. **Apply the formula:** $$\left(\frac{\sqrt{3}}{2}\right)^2 = \frac{(\sqrt{3})^2}{2^2}$$ 4. **Simplify numerator and denominator:** $$\frac{\cancel{(\sqrt{3})^2}}{\cancel{2^2}} = \frac{3}{4}$$ 5. **Final answer:** $$\left(\frac{\sqrt{3}}{2}\right)^2 = \frac{3}{4}$$ This means the square of $\frac{\sqrt{3}}{2}$ is $\frac{3}{4}$.