Question

Find √410 by Estimation

Answer 1

The perfect square near to 410 are 400 and 441 .

i.e. 400 < 410 < 441

20² < 410 < 21²

We guess the answer is between 20 and 21 .

Let us try with 20.3 as. 20 < 20.3 < 21

But

( 20.3 )² = 412.09 > 410

i.e. 20² < 410 < ( 20.3 )²

Let us try 20.2

20.2 × 20.2 = 408.04

408.04 < 410 < 412.09

( 20.2 )² < 410 < ( 20.3 )²

We take √410 as 20.2 approximately .