Question

What will be the digit in the thousand place of (111)2 ?

Answer 1

Correct Question:

$\tt What \ \ will \ \ be \ \ the \ \ digit \ \ in \ \ the \ \ thousand \ \ place \ \ of \ \ (111)^2$

Your Answer:

This Question can be done by different ways.

Way 1: Direct Squaring Method

Square of 111 is 12321

So, Observing the thousand digit

So, the thousand digit is 2

Way 2: Using Identities to find the Square

We can find square by identities instead of using long process

by (a+b)^2 = a^2 + b^2 + 2ab

= (100 + 11)^2

= 100^2 + 11^2 + 2(100)(11)

= 10000 + 121 + 2200

= 12321

So, at thousand digit the number is 2

Way 3: Using property of 11

If you are familiar with the power property of repeating number as 1 then you can answer it very easily. Then there's no need to find square.

So, at the thousand place the digit is 2

Answer 2

This Question can be done by different ways.

Way 1: Direct Squaring Method

Square of $111$ is $12321$

So, Observing the thousand digit

So, a thousand digits is $2$

Way $2$: Using Identities to find the Square

We can find square by identities instead of using long process

by $(a+b)^2 = a^2 + b^2 + 2ab$

$= (100 + 11)^2$

$= 100^2 + 11^2 + 2(100)(11)$

$= 10000 + 121 + 2200$

$= 12321$

So, at the thousand digits, the number is $2$

Way 3: Using the property of $11$

If you are familiar with the power property of repeating numbers as $1$ then you can answer it very easily. Then there's no need to find a square.

So, at the thousand places, the digit is $2$

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