Estimate the square root by looking at the units digit and the pair of numbers which form the hundreds and thousands place

Question

Estimate the square root by looking at the units digit and the pair of numbers which form the hundreds and thousands place

1) 2916
2) 3844
3) 9025
4) 144
5) 676
6) 4225

please provide the reply with steps....please help

Answer 1

144 has 12 as its square root; 676 has 26 as its square root--these ought to be MEMORIZED for quick recognition (we often have problems using Perfect Square numbers, which these are).

 

there are nice square root functions (keys) on even the simplest calculators nowadays; for example, √4225 = 65. this is not surprising since the radicand (4225) ends with 25, the desired integer square root ends in 5, and when looking at 42, the nearest (lesser) square root of that is 6, so that suggests we try 65--which is correct.

 

try this process on 2916 to make the guess; you will always have to verify it, however!