Solve sqrt{150}quad1/40+1/20+1/1.7

$$\sqrt { 150 } \quad \frac { 1 } { 40 } + \frac { 1 } { 20 } + \frac { 1 } { 1.7 }$$

Evaluate

$$\frac{\sqrt{6}}{8}+\frac{217}{340}\approx 0.944421512$$

Solution Steps

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}.

$$5\sqrt{6}\times \frac{1}{40}+\frac{1}{20}+\frac{1}{1.7}$$

Multiply 5 and \frac{1}{40} to get \frac{5}{40}.

$$\frac{5}{40}\sqrt{6}+\frac{1}{20}+\frac{1}{1.7}$$

Reduce the fraction \frac{5}{40} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}\sqrt{6}+\frac{1}{20}+\frac{1}{1.7}$$

Expand \frac{1}{1.7} by multiplying both numerator and the denominator by 10.

$$\frac{1}{8}\sqrt{6}+\frac{1}{20}+\frac{10}{17}$$

Least common multiple of 20 and 17 is 340. Convert \frac{1}{20} and \frac{10}{17} to fractions with denominator 340.

$$\frac{1}{8}\sqrt{6}+\frac{17}{340}+\frac{200}{340}$$

Since \frac{17}{340} and \frac{200}{340} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}\sqrt{6}+\frac{17+200}{340}$$

Add 17 and 200 to get 217.

$$\frac{1}{8}\sqrt{6}+\frac{217}{340}$$

Factor

$$\frac{85 \sqrt{6} + 434}{680} = 0.9444215119655442$$