Solve =0.72*sqrt{200}+0.26*sqrt{150}+0.02*sqrt{100}

$$= 0.72 \times \sqrt { 200 } + 0.26 \times \sqrt { 150 } + 0.02 \times \sqrt { 100 }$$

Evaluate

$$\frac{13\sqrt{6}}{10}+\frac{36\sqrt{2}}{5}+0.2\approx 13.566674315$$

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}.

$$0.72\times 10\sqrt{2}+0.26\sqrt{150}+0.02\sqrt{100}$$

Multiply 0.72 and 10 to get 7.2.

$$7.2\sqrt{2}+0.26\sqrt{150}+0.02\sqrt{100}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$7.2\sqrt{2}+0.26\times 5\sqrt{6}+0.02\sqrt{100}$$

Multiply 0.26 and 5 to get 1.3.

$$7.2\sqrt{2}+1.3\sqrt{6}+0.02\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$7.2\sqrt{2}+1.3\sqrt{6}+0.02\times 10$$

Multiply 0.02 and 10 to get 0.2.

$$7.2\sqrt{2}+1.3\sqrt{6}+0.2$$