How to find whether / if a given number is prime or not?

How to find whether a given number is prime or not?
1) Find largest perfect square less than or equal to this number. Find square root of this perfect square.
2) If the given number is very big you can use long division method of finding square root.
3) Apply divisibility tests for all prime numbers less than or equal to this number. If you do not know divisibility tests for numbers, divide the given number by those prime numbers.
if all the tests fail, the given number is prime number.

Quadratic equations extra sums or questions

Divisibility test for 19 & how to divide by 19 when a number passes the test!

How to find quickly square of numbers from 501 to 531?

To find quickly square of numbers from 501 to 531
1) Add difference from 500 to 250. The addition will form 3 leftmost digits of the square.
2) Square the difference of the number from 500. i.e. subtract 500 from the number & square the difference. This will form next and last three numbers from the square.
If this square is not a three digit number you have to write zero/s to its left to make this square a three digit number.
To make it more clear there are two cases:
a) If the square is a one digit number, you have to put two zeros beofe the square. Ex. 502^2 ---> 2^2 = 004
b) If the square is a two digit number you have to put zero before the square. ex. 505^2 ---> 5^2 = 025
c) If the square of the answer is a 3 digit number (difference from 500 is from 10 to 31) 512^2 --> 12^2 = 144 keep the square as it is.
3) To the right of the number obtained in step 1) , write number obtained in step 2) to get your answer. I mean this is required square of the three digit number from 501 to 531.
4) In above examples,
     502^2= 252,004
     505^2 = 255,025
     512^2 = 262,144.
I think the trick is clear.

My sum on Similarity for 10 th standard

Circle My Sum

Difference between reciprocal of 2 prime numbers (other than 2 &3) is given below. Find the two numbers.
Hint : Product of two prime numbers (other than 2 & 3) is not divisible by their difference.
(i) 2/35
(ii) 4/77
(iii) 4/221
(iv) 6/55
(v) 8/55
(vi) 6/91