Solve 8sqrt{4}*6sqrt{8}*9sqrt{10}

$$8 \sqrt { 4 } \times 6 \sqrt { 8 } \times 9 \sqrt { 10 }$$

Evaluate

$$3456\sqrt{5}\approx 7727.850930239$$

Solution Steps

Factor 8=4\times 2. Rewrite the square root of the product \sqrt{4\times 2} as the product of square roots \sqrt{4}\sqrt{2}.

$$6\times 8\times 9\sqrt{4}\sqrt{4}\sqrt{2}\sqrt{10}$$

Multiply \sqrt{4} and \sqrt{4} to get 4.

$$6\times 8\times 9\times 4\sqrt{2}\sqrt{10}$$

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

$$6\times 8\times 9\times 4\sqrt{2}\sqrt{2}\sqrt{5}$$

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

$$6\times 8\times 9\times 4\times 2\sqrt{5}$$

Multiply 6 and 8 to get 48.

$$48\times 9\times 4\times 2\sqrt{5}$$

Multiply 48 and 9 to get 432.

$$432\times 4\times 2\sqrt{5}$$

Multiply 432 and 4 to get 1728.

$$1728\times 2\sqrt{5}$$

Multiply 1728 and 2 to get 3456.

$$3456\sqrt{5}$$