Solve 3sqrt{3/2*27}

$$3 \sqrt{ \frac{ 3 }{ 2 } \times 27 }$$

Evaluate

$$\frac{27\sqrt{2}}{2}\approx 19.091883092$$

Solution Steps

Express \frac{3}{2}\times 27 as a single fraction.

$$3\sqrt{\frac{3\times 27}{2}}$$

Multiply 3 and 27 to get 81.

$$3\sqrt{\frac{81}{2}}$$

Rewrite the square root of the division \sqrt{\frac{81}{2}} as the division of square roots \frac{\sqrt{81}}{\sqrt{2}}.

$$3\times \frac{\sqrt{81}}{\sqrt{2}}$$

Calculate the square root of 81 and get 9.

$$3\times \frac{9}{\sqrt{2}}$$

Rationalize the denominator of \frac{9}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$3\times \frac{9\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$3\times \frac{9\sqrt{2}}{2}$$

Express 3\times \frac{9\sqrt{2}}{2} as a single fraction.

$$\frac{3\times 9\sqrt{2}}{2}$$

Multiply 3 and 9 to get 27.

$$\frac{27\sqrt{2}}{2}$$