The number of digits in the square root of a perfect square depends in the number of digits in the perfect square. Thus
Number |
Number of the digits in the perfect square |
Number of digits in the square root |
\( \sqrt { 1225 } \) = 35 |
4 |
2= \(\frac { 4 }{ 2 } \) |
\( \sqrt { 961 } \) =31 |
3 |
2= \(\frac { 3+1 }{ 2 } \) |
\( \sqrt { 67600 } \) = 260 |
5 |
3= \(\frac { 5+1}{ 2 } \) |
\( \sqrt { 288369 } \) = 537 |
6 |
3= \(\frac { 6 }{ 2 } \) |
In general, if a perfect square contains n digits then, its square root will contain \(\frac { n }{ 2 } \)
digits, when n is even and \(\frac { n+1 }{ 2 } \) digits, when n is odd.