Solve sqrt{sqrt{3}*3*frac{sqrt{3}}{2}}

$$\sqrt { \sqrt { 3 } \cdot 3 \cdot \frac { \sqrt { 3 } } { 2 } }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

Express 3\times \frac{\sqrt{3}}{2} as a single fraction.

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

Express \frac{3\sqrt{3}}{2}\sqrt{3} as a single fraction.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 3 and 3 to get 9.

$$\sqrt{\frac{9}{2}}$$

Rewrite the square root of the division \sqrt{\frac{9}{2}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2}}.

$$\frac{\sqrt{9}}{\sqrt{2}}$$

Calculate the square root of 9 and get 3.

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

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

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

The square of \sqrt{2} is 2.

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