Solve =sqrt{.1(300-250)^2+.8(250-250)^2+1(200-250)^2}

$$= \sqrt { .1 ( 300 - 250 ) ^ { 2 } + .8 ( 250 - 250 ) ^ { 2 } + 1 ( 200 - 250 ) ^ { 2 } }$$

Evaluate

$$5\sqrt{110}\approx 52.440442409$$

Solution Steps

Subtract 250 from 300 to get 50.

$$\sqrt{0.1\times 50^{2}+0.8\left(250-250\right)^{2}+1\left(200-250\right)^{2}}$$

Calculate 50 to the power of 2 and get 2500.

$$\sqrt{0.1\times 2500+0.8\left(250-250\right)^{2}+1\left(200-250\right)^{2}}$$

Multiply 0.1 and 2500 to get 250.

$$\sqrt{250+0.8\left(250-250\right)^{2}+1\left(200-250\right)^{2}}$$

Subtract 250 from 250 to get 0.

$$\sqrt{250+0.8\times 0^{2}+1\left(200-250\right)^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$\sqrt{250+0.8\times 0+1\left(200-250\right)^{2}}$$

Multiply 0.8 and 0 to get 0.

$$\sqrt{250+0+1\left(200-250\right)^{2}}$$

Add 250 and 0 to get 250.

$$\sqrt{250+1\left(200-250\right)^{2}}$$

Subtract 250 from 200 to get -50.

$$\sqrt{250+1\left(-50\right)^{2}}$$

Calculate -50 to the power of 2 and get 2500.

$$\sqrt{250+1\times 2500}$$

Multiply 1 and 2500 to get 2500.

$$\sqrt{250+2500}$$

Add 250 and 2500 to get 2750.

$$\sqrt{2750}$$

Factor 2750=5^{2}\times 110. Rewrite the square root of the product \sqrt{5^{2}\times 110} as the product of square roots \sqrt{5^{2}}\sqrt{110}. Take the square root of 5^{2}.

$$5\sqrt{110}$$