Square root question ?

 

$\sqrt{37.6765}\approx 6.1381186042630359$

 

Unfortunately, I cannot give you all the decimal places for this answer as it is irrational; any radicand that is not a perfect square yields an irrational result.

$\sqrt{37.6765}$

 

$\sqrt{37\frac{6765}{10000}}$

 

$\sqrt{\frac{376765}{10000}}$

 

$\sqrt{\frac{75353}{2000}}$

 

$\frac{\sqrt{75353}}{\sqrt{2000}}$

 

$\frac{\sqrt{75353}}{\sqrt{400}\sqrt{5}}$

 

$\frac{\sqrt{75353}}{20\sqrt{5}}$

 

$\frac{\sqrt{75353}}{20\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}$

 

$\frac{\sqrt{75353}\sqrt{5}}{20\sqrt{5}\sqrt{5}}$

 

$\frac{\sqrt{376765}}{20\sqrt{5}\sqrt{5}}$

 

$\frac{\sqrt{376765}}{20\sqrt{25}}$

 

$\frac{\sqrt{376765}}{20\times5}$

 

$\frac{\sqrt{376765}}{100}$

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