Question

Find the value of $\sqrt{5}$ correct up to two places of decimals.
A. $2.21$
B. $2.22$
C. $2.23$
D. $2.236$

Answer 1

Hint: We first use the division of square root process to find the square root of 5. We use the concept for both integer and decimal to find the value of $\sqrt{5}$ till the 2-digit place after decimal.

Complete step-by-step solution:
We first have to find and check if the number 5 is a square number or not. 5 is a prime number and that’s why it can’t be broken in factored form.
We take 2 digits as a set from the right end and complete the division. For the decimal form we take the set from the right side of the decimal.
\[\begin{align}
  & 2 \\
 & 2\left| \!{\overline {\,
 \begin{align}
  & \overline{5}.\overline{00}\overline{00} \\
 & \underline{4} \\
 & 1.000 \\
\end{align} \,}} \right. \\
\end{align}\]
Now we have to enter the decimal part. We keep doing the breaking in the set form till 2-digit place after decimal.
\[\begin{align}
  & 2.23 \\
 & 42\left| \!{\overline {\,
 \begin{align}
  & \overline{1}\overline{00}\overline{00}\overline{00} \\
 & \underline{84} \\
 & 1600 \\
\end{align} \,}} \right. \\
 & 443\left| \!{\overline {\,
 \begin{align}
  & 1600\overline{00} \\
 & \underline{1329} \\
 & 27100 \\
\end{align} \,}} \right. \\
\end{align}\]
Therefore, the value of $\sqrt{5}$ is $2.23$.

Note: The long-division method and arranging the set of 2 digits is different for integer and decimal. But taking double for the next division and putting a particular number is the same process for both of them. Since 5 is a non-perfect square number, we will find the value of root 5 using the long division method as shown above.