+2446
\(\sqrt{37.6765}\approx 6.1381186042630359\)
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.
+1904 happygal wants the exact answer, not a decimal answer. If you look at my answer, you will see an exact answer in fraction form.
+2446 Ok, I understand. I'll leave the answer up just in case this user needs the decimal approximation.
+1904 \(\sqrt{37.6765}\)
\(\sqrt{37\frac{6765}{10000}}\)
\(\sqrt{\frac{376765}{10000}}\)
\(\sqrt{\frac{75353}{2000}}\)
\(\frac{\sqrt{75353}}{\sqrt{2000}}\)
\(\frac{\sqrt{75353}}{\sqrt{400}\sqrt{5}}\)
\(\frac{\sqrt{75353}}{20\sqrt{5}}\)
\(\frac{\sqrt{75353}}{20\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}\)
\(\frac{\sqrt{75353}\sqrt{5}}{20\sqrt{5}\sqrt{5}}\)
\(\frac{\sqrt{376765}}{20\sqrt{5}\sqrt{5}}\)
\(\frac{\sqrt{376765}}{20\sqrt{25}}\)
\(\frac{\sqrt{376765}}{20\times5}\)
\(\frac{\sqrt{376765}}{100}\)
.
