Solve f_{3}(u)=0.72*sqrt{200}+0.08*sqrt{110}+0.18*sqrt{190}+0.02*sqrt{100}

$$f _ { 3 } ( u ) = 0.72 \times \sqrt { 200 } + 0.08 \times \sqrt { 110 } + 0.18 \times \sqrt { 190 } + 0.02 \times \sqrt { 100 }$$

Evaluate

$$\frac{2\sqrt{110}}{25}+\frac{9\sqrt{190}}{50}+\frac{36\sqrt{2}}{5}+0.2\approx 13.702513503$$

Solution Steps

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$0.72\times 10\sqrt{2}+0.08\sqrt{110}+0.18\sqrt{190}+0.02\sqrt{100}$$

Multiply 0.72 and 10 to get 7.2.

$$7.2\sqrt{2}+0.08\sqrt{110}+0.18\sqrt{190}+0.02\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$7.2\sqrt{2}+0.08\sqrt{110}+0.18\sqrt{190}+0.02\times 10$$

Multiply 0.02 and 10 to get 0.2.

$$7.2\sqrt{2}+0.08\sqrt{110}+0.18\sqrt{190}+0.2$$