Solving a 'Harvard' University entrance exam question

Added: 2026-05-10

[00:00:00]Hello Friends √(9^9-9^8)=?

[00:00:08]let's have a solution √(9^(8+1)-9^8) since 9=8+1 a^(m+n)=a^m.a^n then It will be √(9^8.9^1-9^8) 9^8 can be common √(9^8(9-1)) √(9^8.8) since √(xy)=√x.√y then √9^8.√8 √9^(4x2).√4x2 since 8=4x2 a^(mxn)=(a^m)^n √(9^4)^2.√4.√2 where square cancels from square root we have 9^4.2.√2 where √4=2 9^(2+2).2.√2 where 4=2+2 9^2.9^2.2.√2 9^2=9x9=81 81.81.2.√2 81x81=6561 we have 6561.2.√2 6561x2=13122 so finally 13122√2 which is our final answer √(9^9-9^8)=13122√2 thanks for watching this video please subscribe this channel to get the notification of my new videos ok bye