Question

Square of 78 by Ishta Sankhya is:
(a) 6084
(b) 7084
(c) 2164
(d) 4524

Answer 1

Hint:In the Ishta Sankhya method of square of 78 we first take the unit digit of 78 then take the product of subtraction of 78 by 8 with the addition of 78 by 8 and add the square of 8 with this product.

Complete step-by-step answer:
We are going to find the square of 78 by Ishta Sankhya method:
First of all take the unit digit of 78 which is 8.
Now, subtracting 8 from 78 we get,
78 – 8 = 70
Now, adding 8 in 78 we get,
78 + 8 =86
Multiplying 70 and 86 will give:
70×86 = 6020
Adding the square of 8 in the above product we get,
6020 + 82
= 6020 + 64
= 6084
Now, writing the above steps in a compact form,
$(78)^2 = (78 – 8)(78 + 8) + 82$
           $ = 6084$
So, the square of 78 is 6084 by Ishta Sankhya.
Hence, the correct option is (a).

Note: For the square of a three digit number say 512 the Ishta Sankhya method will be applied as follows:
As we have taken unit digit in the above two digit number while in the three digit number 512 we will take last two digit numbers i.e. 12 and then take the product of addition of 512 with 12 and the subtraction of 12 from 512 and then add the square of 12 in this product which is shown below:
$(512)^2 = ((512 + 12)(512 – 12)) + (12)^2$.By observing the method we can write general formula as $a^2=((a+b)(a-b))+(b)^2$.Always try to make value of $a$ as multiple of 10,100 or 1000 in order to make simplification easier.