First you have to find the closest perfect squares which, are 8 and 9. We already know that 81 and 64 are the closet, so now  we need to find the middle. So I added 8.5 to 64 to find the middle which is  72.5 ,so we now can elmanate 7.1 , 7.2 , 7.3 ,7.4 ,7.5. Since 77 is closer to 81 we can elmanate 7.6 and 7.7. So it could 7.8 or 7.9