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}

Answer

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Answer

$\boxed{7.3}$ is the approximate value of $\sqrt{53}$ to 1 d.p.

Steps

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.