Question

Using square root table, find the square root
4955 

Answer 1

On prime factorisation:
4955 is equal to 5 \[\times\] which means that \[\sqrt{4955} = \sqrt{5} \times \sqrt{11}\] 

The square root of 991 is not listed in the table; it lists the square roots of all the numbers below 100.
Hence, we have to manipulate the number such that we get the square root of a number less than 100. This can be done in the following manner:

\[\sqrt{4955} = \sqrt{49 . 55 \times 100} = \sqrt{49 . 55} \times 10\] 

Now, we have to find the square root of 49.55.
We have: 

\[\sqrt{49} = 7 and \sqrt{50} = 7 . 071\] 

Their difference is 0.071.
Thus, for the difference of 1 (50 \[-\]49), the difference in the values of the square roots is 0.071.
For the difference of 0.55, the difference in the values of the square roots is:
0.55\[\times\]0.0701 = 0.03905 

\[\therefore\] \[\sqrt{49 . 55} = 7 + 0 . 03905 = 7 . 03905\] 

Finally, we have:

\[\sqrt{4955} = \sqrt{49 . 55} \times 10 = 7 . 03905 \times 10 = 70 . 3905\]