Solving a 'Harvard' University entrance exam question

Added: 2026-05-09

[00:00:00]Hello friends Can you solve this without using any calculator?

[00:00:03]whole square root of five times 4 four times 8 9 √4444488889=?

[00:00:14]we can write whole square root of √4444400000+88888+1 since 88889=88888+1 √44444. 10^5 + 88888 + 1 √44444 (99999 + 1) + 88888 + 1 next step, we can common the values here √4(11111) [9(11111 + 1] + 8(11111) + 1 let suppose that B=11111 then we have √4B (9B+1) + 8B + 1 simplify here √36B^2 + 4B + 8B + 1 next step √36B^2 + 12B + 1 we can write here by factorize √(6B + 1)^2 square will be cancel from square root we have, 6B + 1 since B=11111 we can put here 6 (11111) + 1 we have, 66666 + 1 66667 which is our the correct answer thanks for watching this video please subscribe this channel to get the notification of new video good bye