Example 8. Find the square root of 7.93.
Solving, from equation (31) we have
$$\sqrt{7.93}=\frac{\sqrt{793}}{10}$$

Since $793=61 \times 13$, where 61 and 13 are both prime numbers, from Table 1 we have
Table of square roots of prime numbers below 150
- (Table 1)
\begin{tabular}{c|c||c|c}
\hline$p$ & $\sqrt{p}$ & $p$ & $\sqrt{p}$ \\
\hline 2 & $1.41421356 \cdots$ & 67 & $8.18535277 \cdots$ \\
3 & $1.73205080 \cdots$ & 71 & $8.42614977 \cdots$ \\
5 & $2.23606797 \cdots$ & 73 & $8.54400374 \cdots$ \\
7 & $2.54575131 \cdots$ & 79 & $8.88819441 \cdots$ \\
11 & $3.3166247 \cdots$ & 83 & $9.11043357 \cdots$ \\
13 & $3.60555127 \cdots$ & 89 & $9.43398113 \cdots$ \\
17 & $4.12310562 \cdots$ & 97 & $9.84885780 \cdots$ \\
19 & $4.35889894 \cdots$ & 101 & $10.0498756 \cdots$ \\
23 & $4.79583152 \cdots$ & 103 & $10.1488915 \cdots$ \\
29 & $5.38516480 \cdots$ & 107 & $10.3440804 \cdots$ \\
31 & $5.56776436 \cdots$ & 109 & $10.4403065 \cdots$ \\
37 & $6.0927625 \cdots$ & 113 & $10.6301458 \cdots$ \\
41 & $6.40312423 \cdots$ & 127 & $11.2694276 \cdots$ \\
43 & $6.55743852 \cdots$ & 131 & $11.4455231 \cdots$ \\
47 & $6.85565460 \cdots$ & 137 & $11.7046999 \cdots$ \\
53 & $7.28010988 \cdots$ & 139 & $11.7898261 \cdots$ \\
59 & $7.68114574 \cdots$ & 149 & $12.2065556 \cdots$ \\
61 & $7.81024967 \cdots$ & & \\
\hline
\end{tabular}
Table of cube roots and fifth roots of prime numbers below 60
- (Table 2)
\begin{tabular}{r|l|l|l}
\hline$p$ & $\sqrt[3]{p}$ & $p$ & $\sqrt[5]{p}$ \\
\hline 2 & $1.2599210 \cdots$ & 2 & $1.1486983 \cdots$ \\
3 & $1.4422495 \cdots$ & 3 & $1.2457309 \cdots$ \\
5 & $1.7099759 \cdots$ & 5 & $1.37972966 \cdots$ \\
7 & $1.9129311 \cdots$ & 7 & $1.4757731 \cdots$ \\
11 & $2.22398009 \cdots$ & 11 & $1.6153942 \cdots$ \\
13 & $2.35133468 \cdots$ & 13 & $1.6702776 \cdots$ \\
17 & $2.57128159 \cdots$ & 17 & $1.7623403 \cdots$ \\
19 & $2.66840164 \cdots$ & 19 & $1.8019831 \cdots$ \\
23 & $2.8438669 \cdots$ & 23 & $1.8721712 \cdots$ \\
29 & $3.07231682 \cdots$ & 29 & $1.9610090 \cdots$ \\
31 & $3.14138065 \cdots$ & 31 & $1.9873407 \cdots$ \\
37 & $3.3322218 \cdots$ & 37 & $2.0589241 \cdots$ \\
41 & $3.44821724 \cdots$ & 41 & $2.10163247 \cdots$ \\
43 & $3.50339806 \cdots$ & 43 & $2.1217474 \cdots$ \\
47 & $3.6088260 \cdots$ & 47 & $2.1598300 \cdots$ \\
53 & $3.7562857 \cdots$ & 53 & $2.2123568 \cdots$ \\
59 & $3.8929964 \cdots$ & 59 & $2.2603224 \cdots$ \\
\hline
\end{tabular}
$$\sqrt{61}=7.81024967 \cdots, \quad \sqrt{13}=3.60555127 \cdots$$

From equations (33) and (34) we have
$$\begin{aligned}
\sqrt{7.93} & =\frac{(7.81024967 \cdots) \times(3.60555127 \cdots)}{10} \\
& =2.81602556 \cdots
\end{aligned}$$