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Estimating Square Root

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Consider the following situations: 

1. Deveshi has a square piece of cloth of area 125 cm2. She wants to know whether she can make a handkerchief of side 15 cm. If that is not possible she wants to know what is the maximum length of the side of a handkerchief that can be made from this piece.

2. Meena and Shobha played a game. One told a number and other gave its square root. Meena started first. She said 25 and Shobha answered quickly as 5. Then Shobha said 81 and Meena answered 9. It went on, till at one point Meena gave the number 250. And Shobha could not answer. Then Meena asked Shobha if she could atleast tell a number whose square is closer to 250.
In all such cases we need to estimate the square root. 
We know that 100 < 250 < 400 and `sqrt 100` =10 and `sqrt 400` = 20 
So,  10 < `sqrt 250` < 20
But still we are not very close to the square number. 

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