Question

Method to solve
Square root of 71x72x73x74+1

Answer 1

your answer is 5,225 by root
method:
multiply 71*72*73*74 and add +1
now u will get an answer
now take root of it
hence,u will get its ans

Answer 2

Solution :-

Here. consider the fact that the product of 4 consecutive numbers + 1 is perfect square.

So, let x = 71

⇒ (71)*(72)*(73)*(74) + 1 = x(x + 1) (x + 2) (x + 3) +1 

⇒ (x² + 3x)(x² + 3x + 2) + 1

⇒ (x² + 3x)² + 2(x² + 3x) + 1

⇒ (x² + 3x + 1)²

⇒ Square root of (x² + 3x + 1)² = x² + 3x + 1

Here, x = 71

Therefore, square root is = (71)² + (3*71) + 1

⇒ 5041 + 213 + 1 

= 5255

Answer.