Question

The value of $(110{)}^2$ is _______

• A. 12050
• B. 12100
• C. 13526
• D. 11100

Answer 1

The correct option is B 12100

To find the square of 110, we need to follow the given steps:
Step 1: Subtract 100 from 110.
We get 10.

Step 2: Add 10 to 110.
We get 120.

Step 3: Find the square of 10. Consider the digits in units and tens place and the digit in the hundreds place will be added to 120.
i.e., We consider only last two digits, 00, of 100 and the 1 will be added to 120 (120+1=121).

Hence, we get 120 + 1 = 121 and 00 from 100 will be placed to the right of 121.


So, the square of 110 = 12100

[Alternate method:
$(110{)}^2=(100+10{)}^2={100}^2+2\left(100\right)\left(10\right)+{10}^2=10000+2000+100=12100]$