Solve (3/4sqrt{15})(16sqrt{5})

$$( \frac { 3 } { 4 } \sqrt { 15 } ) ( 16 \sqrt { 5 } )$$

Evaluate

$$60\sqrt{3}\approx 103.923048454$$

Solution Steps

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{3}{4}\sqrt{5}\sqrt{3}\times 16\sqrt{5}$$

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

$$\frac{3}{4}\times 5\times 16\sqrt{3}$$

Express \frac{3}{4}\times 5 as a single fraction.

$$\frac{3\times 5}{4}\times 16\sqrt{3}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{4}\times 16\sqrt{3}$$

Express \frac{15}{4}\times 16 as a single fraction.

$$\frac{15\times 16}{4}\sqrt{3}$$

Multiply 15 and 16 to get 240.

$$\frac{240}{4}\sqrt{3}$$

Divide 240 by 4 to get 60.

$$60\sqrt{3}$$