Solve sqrt{10(10-2)(10-5)(10-7)}

$$\sqrt{ 10(10-2)(10-5)(10-7) }$$

Evaluate

$$20\sqrt{3}\approx 34.641016151$$

Solution Steps

Subtract 2 from 10 to get 8.

$$\sqrt{10\times 8\left(10-5\right)\left(10-7\right)}$$

Multiply 10 and 8 to get 80.

$$\sqrt{80\left(10-5\right)\left(10-7\right)}$$

Subtract 5 from 10 to get 5.

$$\sqrt{80\times 5\left(10-7\right)}$$

Multiply 80 and 5 to get 400.

$$\sqrt{400\left(10-7\right)}$$

Subtract 7 from 10 to get 3.

$$\sqrt{400\times 3}$$

Multiply 400 and 3 to get 1200.

$$\sqrt{1200}$$

Factor 1200=20^{2}\times 3. Rewrite the square root of the product \sqrt{20^{2}\times 3} as the product of square roots \sqrt{20^{2}}\sqrt{3}. Take the square root of 20^{2}.

$$20\sqrt{3}$$