Solve sqrt{16(16-12)(16-12)(16-8)}

$$\sqrt { 16 ( 16 - 12 ) ( 16 - 12 ) ( 16 - 8 ) }$$

Evaluate

$$32\sqrt{2}\approx 45.254833996$$

Solution Steps

Multiply 16-12 and 16-12 to get \left(16-12\right)^{2}.

$$\sqrt{16\left(16-12\right)^{2}\left(16-8\right)}$$

Subtract 12 from 16 to get 4.

$$\sqrt{16\times 4^{2}\left(16-8\right)}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16\times 16\left(16-8\right)}$$

Multiply 16 and 16 to get 256.

$$\sqrt{256\left(16-8\right)}$$

Subtract 8 from 16 to get 8.

$$\sqrt{256\times 8}$$

Multiply 256 and 8 to get 2048.

$$\sqrt{2048}$$

Factor 2048=32^{2}\times 2. Rewrite the square root of the product \sqrt{32^{2}\times 2} as the product of square roots \sqrt{32^{2}}\sqrt{2}. Take the square root of 32^{2}.

$$32\sqrt{2}$$