Solve sqrt{2016div19-102.01}

$$\sqrt{ 2016 \div 19-102.01 }$$

Evaluate

$$\frac{\sqrt{147839}}{190}\approx 2.023675655$$

Solution Steps

Convert decimal number 102.01 to fraction \frac{10201}{100}.

$$\sqrt{\frac{2016}{19}-\frac{10201}{100}}$$

Least common multiple of 19 and 100 is 1900. Convert \frac{2016}{19} and \frac{10201}{100} to fractions with denominator 1900.

$$\sqrt{\frac{201600}{1900}-\frac{193819}{1900}}$$

Since \frac{201600}{1900} and \frac{193819}{1900} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{201600-193819}{1900}}$$

Subtract 193819 from 201600 to get 7781.

$$\sqrt{\frac{7781}{1900}}$$

Rewrite the square root of the division \sqrt{\frac{7781}{1900}} as the division of square roots \frac{\sqrt{7781}}{\sqrt{1900}}.

$$\frac{\sqrt{7781}}{\sqrt{1900}}$$

Factor 1900=10^{2}\times 19. Rewrite the square root of the product \sqrt{10^{2}\times 19} as the product of square roots \sqrt{10^{2}}\sqrt{19}. Take the square root of 10^{2}.

$$\frac{\sqrt{7781}}{10\sqrt{19}}$$

Rationalize the denominator of \frac{\sqrt{7781}}{10\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{\sqrt{7781}\sqrt{19}}{10\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{\sqrt{7781}\sqrt{19}}{10\times 19}$$

To multiply \sqrt{7781} and \sqrt{19}, multiply the numbers under the square root.

$$\frac{\sqrt{147839}}{10\times 19}$$

Multiply 10 and 19 to get 190.

$$\frac{\sqrt{147839}}{190}$$