Question

how many non perfect square number lies between 30² and 31² ?​

Answer 1

Answer:

Step-by-step explanation:

Numbers between

31² & 33²

Vol 86

are 33² -31² - 1

= (33 +31)(33 - 31) - 1

= 64 * 2 - 1

= 128 - 1

= 127

but in between 31² & 33², 32² would be perfect square

=> non perfect square numbers = 127-1 => non perfect square numbers between

31² & 33²= 126

Or use formula that 2n numbers are between n² & (n+1)²

perfect square between 312 & 33² is 32²

numbers between 31² & 32² = 2 * 31 = 62 numbers between 32² & 33² = 2 * 32 = 64

non perfect Square number between 31² & 33²= 62 +64 = 126