Solve O*17+3sqrt{(1-017)/15}

$$O \cdot 17 + 3 \sqrt { \frac { ( 1 - 017 ) } { 15 } }$$

Evaluate

$$17O+\frac{\sqrt{15}}{5}$$

Short Solution Steps

Multiply 0 and 17 to get 0.

$$O\times 17+3\sqrt{\frac{1-0}{15}}$$

Subtract 0 from 1 to get 1.

$$O\times 17+3\sqrt{\frac{1}{15}}$$

Rewrite the square root of the division \sqrt{\frac{1}{15}} as the division of square roots \frac{\sqrt{1}}{\sqrt{15}}.

$$O\times 17+3\times \frac{\sqrt{1}}{\sqrt{15}}$$

Calculate the square root of 1 and get 1.

$$O\times 17+3\times \frac{1}{\sqrt{15}}$$

Rationalize the denominator of \frac{1}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

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

The square of \sqrt{15} is 15.

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

Cancel out 15, the greatest common factor in 3 and 15.

$$O\times 17+\frac{\sqrt{15}}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply O\times 17 times \frac{5}{5}.

$$\frac{5O\times 17}{5}+\frac{\sqrt{15}}{5}$$

Since \frac{5O\times 17}{5} and \frac{\sqrt{15}}{5} have the same denominator, add them by adding their numerators.

$$\frac{5O\times 17+\sqrt{15}}{5}$$

Do the multiplications in 5O\times 17+\sqrt{15}.

$$\frac{85O+\sqrt{15}}{5}$$

Differentiate w.r.t. O

$$17$$