Square Root = Sq. Root of Nearest Perfect Square + {difference of the given number from the nearest perfect square / 2 x (Sq. Root of Nearest Perfect Square)}
Example 1 : Square Root of 57.
= 8 + (57-64) / 2 x 8 (since the perfect square closest to 57 is 64; we will take square root of 64 i.e. 8 for calculations)
= 8 – 7/2×8
=8 – 7/16
= 7.56 (approx).
= 8 + (57-64) / 2 x 8 (since the perfect square closest to 57 is 64; we will take square root of 64 i.e. 8 for calculations)
= 8 – 7/2×8
=8 – 7/16
= 7.56 (approx).
The exact answer is 7.5498
Example 2 : Square Root of 440
= 20 + (410-400) / 2 x 20 (since the perfect square closest to 440 is 441; we will take square root of 441 i.e. 21 for calculations)
= 20+10/40
= 20.25 (approx).
The exact answer is 20.248
= 20 + (410-400) / 2 x 20 (since the perfect square closest to 440 is 441; we will take square root of 441 i.e. 21 for calculations)
= 20+10/40
= 20.25 (approx).
The exact answer is 20.248
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