Solve sqrt{32(32-12)(32-12)(32-8)}

$$\sqrt { 32 ( 32 - 12 ) ( 32 - 12 ) ( 32 - 8 ) }$$

Evaluate

$$320\sqrt{3}\approx 554.256258422$$

Solution Steps

Multiply 32-12 and 32-12 to get \left(32-12\right)^{2}.

$$\sqrt{32\left(32-12\right)^{2}\left(32-8\right)}$$

Subtract 12 from 32 to get 20.

$$\sqrt{32\times 20^{2}\left(32-8\right)}$$

Calculate 20 to the power of 2 and get 400.

$$\sqrt{32\times 400\left(32-8\right)}$$

Multiply 32 and 400 to get 12800.

$$\sqrt{12800\left(32-8\right)}$$

Subtract 8 from 32 to get 24.

$$\sqrt{12800\times 24}$$

Multiply 12800 and 24 to get 307200.

$$\sqrt{307200}$$

Factor 307200=320^{2}\times 3. Rewrite the square root of the product \sqrt{320^{2}\times 3} as the product of square roots \sqrt{320^{2}}\sqrt{3}. Take the square root of 320^{2}.

$$320\sqrt{3}$$