Solve sqrt{8(3/2)^3-27/4(frac{3{2})^3-9}}

$$\sqrt { \frac { 8 ( \frac { 3 } { 2 } ) ^ { 3 } - 27 } { 4 ( \frac { 3 } { 2 } ) ^ { 3 } - 9 } }$$

Evaluate

$$0$$

Solution Steps

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\sqrt{\frac{8\times \frac{27}{8}-27}{4\times \left(\frac{3}{2}\right)^{3}-9}}$$

Cancel out 8 and 8.

$$\sqrt{\frac{27-27}{4\times \left(\frac{3}{2}\right)^{3}-9}}$$

Subtract 27 from 27 to get 0.

$$\sqrt{\frac{0}{4\times \left(\frac{3}{2}\right)^{3}-9}}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\sqrt{\frac{0}{4\times \frac{27}{8}-9}}$$

Express 4\times \frac{27}{8} as a single fraction.

$$\sqrt{\frac{0}{\frac{4\times 27}{8}-9}}$$

Multiply 4 and 27 to get 108.

$$\sqrt{\frac{0}{\frac{108}{8}-9}}$$

Reduce the fraction \frac{108}{8} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{0}{\frac{27}{2}-9}}$$

Convert 9 to fraction \frac{18}{2}.

$$\sqrt{\frac{0}{\frac{27}{2}-\frac{18}{2}}}$$

Since \frac{27}{2} and \frac{18}{2} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{0}{\frac{27-18}{2}}}$$

Subtract 18 from 27 to get 9.

$$\sqrt{\frac{0}{\frac{9}{2}}}$$

Zero divided by any non-zero number gives zero.

$$\sqrt{0}$$

Calculate the square root of 0 and get 0.

$$0$$

Factor

$$0$$