97. Let a, b be two single digit natural numbers and 'aa bb' is a four

1.	97. Let a, b be two single digit natural numbers and 'aa bb' is a four digit number which is perfect square ofnatural number, such that a + b 2k + 1. Find k.
Answer» the 4 digit number is aabb now for a no. to be divisible by 11, the difference of off odd place number and even place number is multiple of 11 here it is (a+b) -(a+b) = 0 which is a multiple of 11 , so the number aabb is always divisible by 11 so 11 = 2k+1 => 2k = 10 or k = 10/2 = 5

97. Let a, b be two single digit natural numbers and 'aa bb' is a four digit number which is perfect square ofnatural number, such that a + b 2k + 1. Find k.

Answer»

the 4 digit number is aabb

now for a no. to be divisible by 11, the difference of off odd place number and even place number is multiple of 11

here it is (a+b) -(a+b) = 0

which is a multiple of 11 , so the number aabb is always divisible by 11

so 11 = 2k+1 => 2k = 10 or k = 10/2 = 5