Solve =sqrt{90(90-80)(90-70)(90-30)}

$$= \sqrt { 90 ( 90 - 80 ) ( 90 - 70 ) ( 90 - 30 ) }$$

Evaluate

$$600\sqrt{3}\approx 1039.230484541$$

Solution Steps

Subtract 80 from 90 to get 10.

$$\sqrt{90\times 10\left(90-70\right)\left(90-30\right)}$$

Multiply 90 and 10 to get 900.

$$\sqrt{900\left(90-70\right)\left(90-30\right)}$$

Subtract 70 from 90 to get 20.

$$\sqrt{900\times 20\left(90-30\right)}$$

Multiply 900 and 20 to get 18000.

$$\sqrt{18000\left(90-30\right)}$$

Subtract 30 from 90 to get 60.

$$\sqrt{18000\times 60}$$

Multiply 18000 and 60 to get 1080000.

$$\sqrt{1080000}$$

Factor 1080000=600^{2}\times 3. Rewrite the square root of the product \sqrt{600^{2}\times 3} as the product of square roots \sqrt{600^{2}}\sqrt{3}. Take the square root of 600^{2}.

$$600\sqrt{3}$$