If 11 × 11 = 4,

22 × 22 = 16,

33 × 33 = 36, and

44 × 44=64,

then what is the value of 55 × 55?

There are many ways to solve this problem. Here I am sharing one of the technique that hit my mind first. Follow step by step instructions to get solution.

As we are provided with basic data (that may or may not be true for real calculations), so I am not going to assume anything or putting any signs.

It is provided that, 11 X 11 = 4 ….let it be equation no. 1

also, 22 X 22 = 16 …….given

=> (11 X 2) X (11 X 2)

=> (11 X 11) X (2 X 2) ……..equation no. 2

=> 4 X (2 X 2) ……..from equation no. 1

=> 4 X 4 = 16

similarly, 33 X 33 = (11 X 3) X (11 X 3)= (11 X11) X (3 X 3)= 4 X (3 X 3) = 4 X 9 = 36

also, 44 X 44 = (11 X 4) X (11 X 4) = (11 X 11) X (4 X4) = 4 X (4 X 4) = 4 X 16 = 64

=> 55 x 55 = (11 X 11) X (5 X 5)= 100

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