Home
Class 12
MATHS
A natural number n is chosen strictly be...

A natural number n is chosen strictly between two consecutive perfect square. The smaller of these two squares is obtained by subtracting k from n and the larger one is obtained by adding l to n. Prove that nkl is a perfect square.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - I)|22 Videos
  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise HLP|34 Videos
  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SSP|55 Videos

Similar Questions

Explore conceptually related problems

Prove that sqrt(n) is not a rational number. if n is not a perfect square.

Prove that sqrt(n) is not a rational number. if n is not a perfect square.

Find the least number which must be added to 18,265 to obtain a perfect square.

Find the least number which must be subtracted from 5607 to make a perfect square.

Find the greatest number of two digits which is a perfect square.

Find the least number that must be subtracted from 2433 so that the remainder isa perfect square.

The difference of the squares of two consecutive even natural numbers is 92. Taking x as the smaller of the two numbers, form an equation in x and hence find the larger of the two.

The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also find the square root of the perfect square so obtained.

Find the least number which must be subtracted from 18265 to make it a perfect square. Also, find the square root of the resulting number.