Solve 3^3sqrt{64*8*729}

$${ 3 }^{ 3 } \sqrt{ 64 \times 8 \times 729 }$$

Evaluate

$$11664\sqrt{2}\approx 16495.38699152$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$27\sqrt{64\times 8\times 729}$$

Multiply 64 and 8 to get 512.

$$27\sqrt{512\times 729}$$

Multiply 512 and 729 to get 373248.

$$27\sqrt{373248}$$

Factor 373248=432^{2}\times 2. Rewrite the square root of the product \sqrt{432^{2}\times 2} as the product of square roots \sqrt{432^{2}}\sqrt{2}. Take the square root of 432^{2}.

$$27\times 432\sqrt{2}$$

Multiply 27 and 432 to get 11664.

$$11664\sqrt{2}$$