\( \sqrt{37845}=\sqrt{3^2 \times 5 \times 29^2} \)
\( \sqrt{3^2 \times 5 \times 29^2}=\sqrt{3^2} \sqrt{5} \sqrt{29^2} \)
\( \sqrt{3^2} \sqrt{5} \sqrt{29^2}=3 \times \sqrt{5} \times 29=87 \sqrt{5} \)
we know \( \sqrt{5}=2.23606 \) thus:
\( \sqrt{37845}=87 \times 2.23606=194.537 \)
