Problem
The table below can be used to find the approximate value of $\sqrt{53}$. a) What exact values should replace $A, B$ and $C$ ? b) Find the approximate value of $\sqrt{53}$ to 1 d.p. \begin{tabular}{|c|c|c|} \hline$x$ & $x^{2}$ & Comment \\ \hline 7 & 49 & Too low \\ 8 & 64 & Too high \\ 7.5 & 56.25 & Too high \\ 7.2 & & \\ 7.3 & & \\ 7.25 & & \\ \hline \end{tabular}
Solution
Step 1 ：Find the values of $x^2$ for $x = 7.2, 7.3,$ and $7.25$
Step 2 ：\(7.2^2 = 51.84\)
Step 3 ：\(7.3^2 = 53.29\)
Step 4 ：\(7.25^2 = 52.5625\)
Step 5 ：Compare the values to 53 and determine which is closest
Step 6 ：\(\boxed{7.3}\) is the approximate value of \(\sqrt{53}\) to 1 d.p.
