Question

Which of the following is the greatest?

\(\sqrt 59 -\sqrt 51 , \sqrt 37 - \sqrt 29, \sqrt 87 - \sqrt 79 \ and \sqrt 79 - \sqrt 71\)

1. \(\sqrt 37 - \sqrt 29\)
2. \(\sqrt 59 - \sqrt 51\)
3. \(\sqrt 87 - \sqrt 79\)
4. \(\sqrt 79 - \sqrt 71\)

Answer 1

Correct Answer - Option 1 : \(\sqrt 37 - \sqrt 29\)

Given:

\(√ 59 -√ 51 , √ 37 - √ 29, √ 87 - √ 79 \ and √ 79 - √ 71\)

Concept Used:

When the difference between the numbers are the same then the smallest number becomes the greatest

Calculation:

To solve this type of question first compare the difference of numbers without taking square root.

⇒ 59 - 51 = 8

⇒ 37 - 29 = 8

⇒ 87 - 79 = 8

⇒ 79 - 71 = 8

Here we will see that the difference is the same in all cases.

Then the smallest number becomes greatest.

Here, \(\sqrt 37 - \sqrt 29\) is the smaller one in comparison to all numbers

∴ \(\sqrt 37 - \sqrt 29\) is the greatest.