INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

March 20, 2020

Squares and Square roots | HANOI 2018

Try this beautiful problem from American Invitational Mathematics Examination, HANOI, 2018 based on Squares and square roots.

Squares and square roots - HANOI 2018

Let a=\((\sqrt2+\sqrt3+\sqrt6)(\sqrt2+\sqrt3-\sqrt6)(\sqrt3+\sqrt6-\sqrt2)(\sqrt6+\sqrt2-\sqrt3)\)

b=\((\sqrt2+\sqrt3+\sqrt5)(\sqrt2+\sqrt3-\sqrt5)(\sqrt3+\sqrt5-\sqrt2)(\sqrt5+\sqrt2-\sqrt3)\). The difference a-b belongs to the set

  • is [-4,0)
  • is {6}
  • is [-8,-6]
  • cannot be determined from the given information

Key Concepts


Squares and square roots

Number Theory

Check the Answer

Answer: is [-4,0).

HANOI, 2018

Elementary Number Theory by David Burton

Try with Hints

First hint


Second Hint

We get a-b=2(2+3)(6-5)-\(6^{2}+5^{2}\)=-1.

Final Step

Then a-b belongs to [-4,0).

Subscribe to Cheenta at Youtube

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.