Solve sqrt{(1060.9489-112.37^2div12)div11}

$$\sqrt{ (1060.9489- { 112.37 }^{ 2 } \div 12) \div 11 }$$

Evaluate

$$\frac{\sqrt{34442067}}{6600}\approx 0.889202486$$

Solution Steps

Calculate 112.37 to the power of 2 and get 12627.0169.

$$\sqrt{\frac{1060.9489-\frac{12627.0169}{12}}{11}}$$

Expand \frac{12627.0169}{12} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{1060.9489-\frac{126270169}{120000}}{11}}$$

Convert decimal number 1060.9489 to fraction \frac{10609489}{10000}.

$$\sqrt{\frac{\frac{10609489}{10000}-\frac{126270169}{120000}}{11}}$$

Least common multiple of 10000 and 120000 is 120000. Convert \frac{10609489}{10000} and \frac{126270169}{120000} to fractions with denominator 120000.

$$\sqrt{\frac{\frac{127313868}{120000}-\frac{126270169}{120000}}{11}}$$

Since \frac{127313868}{120000} and \frac{126270169}{120000} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{127313868-126270169}{120000}}{11}}$$

Subtract 126270169 from 127313868 to get 1043699.

$$\sqrt{\frac{\frac{1043699}{120000}}{11}}$$

Express \frac{\frac{1043699}{120000}}{11} as a single fraction.

$$\sqrt{\frac{1043699}{120000\times 11}}$$

Multiply 120000 and 11 to get 1320000.

$$\sqrt{\frac{1043699}{1320000}}$$

Rewrite the square root of the division \sqrt{\frac{1043699}{1320000}} as the division of square roots \frac{\sqrt{1043699}}{\sqrt{1320000}}.

$$\frac{\sqrt{1043699}}{\sqrt{1320000}}$$

Factor 1320000=200^{2}\times 33. Rewrite the square root of the product \sqrt{200^{2}\times 33} as the product of square roots \sqrt{200^{2}}\sqrt{33}. Take the square root of 200^{2}.

$$\frac{\sqrt{1043699}}{200\sqrt{33}}$$

Rationalize the denominator of \frac{\sqrt{1043699}}{200\sqrt{33}} by multiplying numerator and denominator by \sqrt{33}.

$$\frac{\sqrt{1043699}\sqrt{33}}{200\left(\sqrt{33}\right)^{2}}$$

The square of \sqrt{33} is 33.

$$\frac{\sqrt{1043699}\sqrt{33}}{200\times 33}$$

To multiply \sqrt{1043699} and \sqrt{33}, multiply the numbers under the square root.

$$\frac{\sqrt{34442067}}{200\times 33}$$

Multiply 200 and 33 to get 6600.

$$\frac{\sqrt{34442067}}{6600}$$