Solve (2/3sqrt{5})(3/4sqrt{10})(1/2sqrt{15})

$$( \frac { 2 } { 3 } \sqrt { 5 } ) ( \frac { 3 } { 4 } \sqrt { 10 } ) ( \frac { 1 } { 2 } \sqrt { 15 } )$$

Evaluate

$$\frac{5\sqrt{30}}{4}\approx 6.846531969$$

Solution Steps

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\frac{2}{3}\sqrt{5}\times \frac{3}{4}\sqrt{5}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{2}{3}\times 5\times \frac{3}{4}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Express \frac{2}{3}\times 5 as a single fraction.

$$\frac{2\times 5}{3}\times \frac{3}{4}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{3}\times \frac{3}{4}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Multiply \frac{10}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 3}{3\times 4}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Cancel out 3 in both numerator and denominator.

$$\frac{10}{4}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}\sqrt{2}\times \frac{1}{2}\sqrt{15}$$

Multiply \frac{5}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 1}{2\times 2}\sqrt{2}\sqrt{15}$$

Do the multiplications in the fraction \frac{5\times 1}{2\times 2}.

$$\frac{5}{4}\sqrt{2}\sqrt{15}$$

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{5}{4}\sqrt{30}$$