Solve sqrt{27}*3sqrt{12}*5/8sqrt{3}

$$\sqrt { 27 } \times 3 \sqrt { 12 } \times \frac { 5 } { 8 } \sqrt { 3 }$$

Evaluate

$$\frac{135\sqrt{3}}{4}\approx 58.456714755$$

Solution Steps

Factor 27=3\times 9. Rewrite the square root of the product \sqrt{3\times 9} as the product of square roots \sqrt{3}\sqrt{9}.

$$3\sqrt{3}\sqrt{9}\sqrt{12}\times \frac{5}{8}\sqrt{3}$$

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

$$3\times 3\sqrt{12}\times \frac{5}{8}\sqrt{9}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{12}\times \frac{5}{8}\sqrt{9}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$9\times 2\sqrt{3}\times \frac{5}{8}\sqrt{9}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{3}\times \frac{5}{8}\sqrt{9}$$

Express 18\times \frac{5}{8} as a single fraction.

$$\frac{18\times 5}{8}\sqrt{3}\sqrt{9}$$

Multiply 18 and 5 to get 90.

$$\frac{90}{8}\sqrt{3}\sqrt{9}$$

Reduce the fraction \frac{90}{8} to lowest terms by extracting and canceling out 2.

$$\frac{45}{4}\sqrt{3}\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$\frac{45}{4}\sqrt{3}\times 3$$

Express \frac{45}{4}\times 3 as a single fraction.

$$\frac{45\times 3}{4}\sqrt{3}$$

Multiply 45 and 3 to get 135.

$$\frac{135}{4}\sqrt{3}$$