Solve O*17+3sqrt{(1-0.17)/15}

$$O \cdot 17 + 3 \sqrt { \frac { ( 1 - 0.17 ) } { 15 } }$$

Evaluate

$$17O+\frac{\sqrt{1245}}{50}$$

Short Solution Steps

Subtract 0.17 from 1 to get 0.83.

$$O\times 17+3\sqrt{\frac{0.83}{15}}$$

Expand \frac{0.83}{15} by multiplying both numerator and the denominator by 100.

$$O\times 17+3\sqrt{\frac{83}{1500}}$$

Rewrite the square root of the division \sqrt{\frac{83}{1500}} as the division of square roots \frac{\sqrt{83}}{\sqrt{1500}}.

$$O\times 17+3\times \frac{\sqrt{83}}{\sqrt{1500}}$$

Factor 1500=10^{2}\times 15. Rewrite the square root of the product \sqrt{10^{2}\times 15} as the product of square roots \sqrt{10^{2}}\sqrt{15}. Take the square root of 10^{2}.

$$O\times 17+3\times \frac{\sqrt{83}}{10\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{83}}{10\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$O\times 17+3\times \frac{\sqrt{83}\sqrt{15}}{10\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$O\times 17+3\times \frac{\sqrt{83}\sqrt{15}}{10\times 15}$$

To multiply \sqrt{83} and \sqrt{15}, multiply the numbers under the square root.

$$O\times 17+3\times \frac{\sqrt{1245}}{10\times 15}$$

Multiply 10 and 15 to get 150.

$$O\times 17+3\times \frac{\sqrt{1245}}{150}$$

Cancel out 150, the greatest common factor in 3 and 150.

$$O\times 17+\frac{\sqrt{1245}}{50}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply O\times 17 times \frac{50}{50}.

$$\frac{50O\times 17}{50}+\frac{\sqrt{1245}}{50}$$

Since \frac{50O\times 17}{50} and \frac{\sqrt{1245}}{50} have the same denominator, add them by adding their numerators.

$$\frac{50O\times 17+\sqrt{1245}}{50}$$

Do the multiplications in 50O\times 17+\sqrt{1245}.

$$\frac{850O+\sqrt{1245}}{50}$$

Differentiate w.r.t. O

$$17$$