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: The square root of any positive integer can be found by various methods such as, Average method, Number line method and Long division method. Here in this given problem ‘5’ is not a perfect square so we have to use any of the three methods to find its root. Here we are going to use a long division method to find the root value. We have some steps to be followed for finding the root value.

Complete step-by-step solution:
We can outline the steps as below,
Step 1: We can draw lines over pairs of digits from right to left.
Step 2: Let us find the greatest number whose square is less than or equal to the digits in the first group.
Step 3: We can take this number as the divisor and the quotient of the first group and find the reminder.
Step 4: Now we can move the digits from the second group besides the reminder to get the new dividend.
Step 5: We can double the first divisor and bring it down as the new divisor.
Step 6: Let us complete the divisor and continue the division.
Step 7: Now we can put the decimal part in the square root as soon as the integral part is exhausted.
Step 8: We can repeat the process till the remainder becomes zero.
\[\dfrac{\begin{align}
  & 2 \\
 & 2 \\
\end{align}}{\dfrac{\begin{align}
  & 42 \\
 & 2 \\
\end{align}}{\dfrac{443}{{}}}}\overset{2.23}{\overline{\left){\dfrac{\begin{align}
  & 5.0000 \\
 & 4\downarrow \downarrow \\
\end{align}}{\dfrac{\begin{align}
  & 100 \\
 & \text{ 84} \\
\end{align}}{\dfrac{\begin{align}
  & \text{ }1600 \\
 & \text{ 1329} \\
\end{align}}{\text{ 27}}}}}\right.}}\]
The answer is option C. 2.23.

Note: Always remember the steps for the long division method. We can also use methods like, Number line and Average method. Students may be confused that the option D. 2.236 is correct, but the question is “upto two decimal points”. Therefore, the correct answer is option C. 2.23.