Solve 464sqrt{2}*3/4sqrt{6}=

$$464 \sqrt { 2 } \times \frac { 3 } { 4 } \sqrt { 6 } =$$

Evaluate

$$696\sqrt{3}\approx 1205.507362068$$

Solution Steps

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$464\sqrt{2}\times \frac{3}{4}\sqrt{2}\sqrt{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$464\times 2\times \frac{3}{4}\sqrt{3}$$

Multiply 464 and 2 to get 928.

$$928\times \frac{3}{4}\sqrt{3}$$

Express 928\times \frac{3}{4} as a single fraction.

$$\frac{928\times 3}{4}\sqrt{3}$$

Multiply 928 and 3 to get 2784.

$$\frac{2784}{4}\sqrt{3}$$

Divide 2784 by 4 to get 696.

$$696\sqrt{3}$$