Solve sqrt{3^7*4^2*5}

$$\sqrt { 3 ^ { 7 } \times 4 ^ { 2 } \times 5 }$$

Evaluate

$$108\sqrt{15}\approx 418.28220139$$

Solution Steps

Calculate 3 to the power of 7 and get 2187.

$$\sqrt{2187\times 4^{2}\times 5}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{2187\times 16\times 5}$$

Multiply 2187 and 16 to get 34992.

$$\sqrt{34992\times 5}$$

Multiply 34992 and 5 to get 174960.

$$\sqrt{174960}$$

Factor 174960=108^{2}\times 15. Rewrite the square root of the product \sqrt{108^{2}\times 15} as the product of square roots \sqrt{108^{2}}\sqrt{15}. Take the square root of 108^{2}.

$$108\sqrt{15}$$