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what is the exact square root of 37.6765? 

happygal  Aug 24, 2017
 #1
avatar+2139 
+1

 

\(\sqrt{37.6765}\approx 6.1381186042630359\)

 

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.

TheXSquaredFactor  Aug 24, 2017
 #3
avatar+1841 
0

happygal wants the exact answer, not a decimal answer.  If you look at my answer, you will see an exact answer in fraction form.

gibsonj338  Aug 24, 2017
 #4
avatar+2139 
0

Ok, I understand. I'll leave the answer up just in case this user needs the decimal approximation.

TheXSquaredFactor  Aug 24, 2017
 #2
avatar+1841 
0

\(\sqrt{37.6765}\)

 

\(\sqrt{37\frac{6765}{10000}}\)

 

\(\sqrt{\frac{376765}{10000}}\)

 

\(\sqrt{\frac{75353}{2000}}\)

 

\(\frac{\sqrt{75353}}{\sqrt{2000}}\)

 

\(\frac{\sqrt{75353}}{\sqrt{400}\sqrt{5}}\)

 

\(\frac{\sqrt{75353}}{20\sqrt{5}}\)

 

\(\frac{\sqrt{75353}}{20\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}\)

 

\(\frac{\sqrt{75353}\sqrt{5}}{20\sqrt{5}\sqrt{5}}\)

 

\(\frac{\sqrt{376765}}{20\sqrt{5}\sqrt{5}}\)

 

\(\frac{\sqrt{376765}}{20\sqrt{25}}\)

 

\(\frac{\sqrt{376765}}{20\times5}\)

 

\(\frac{\sqrt{376765}}{100}\)

gibsonj338  Aug 24, 2017

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