Show that the square roots of two successive natural numbers greater than `N^2` differ by less than `1/(2N)dot`

Write a prime number greater than 91 but less than 100.

The roots alpha and beta of a quadratic equation are the square of two consecutive natural numbers.The geometric mean of the two roots. is 1 greater than the difference of the roots.If alpha and beta lies between the roots of x^(2)-cx+1=0 then find the minimum integral value of c.

a number is as much greater than 21 as it is less than 71. find the number.

The square root of a positive number less than 100 lies between:

The sum of prime number that are greater than 60, but less than 70 is