Oh, dude, the square root of 93 is between 9 and 10, so the integers closest to it are 9 and 10. It's like when you're trying to find the closest parking spot to the mall entrance - you pick the one that's right there, not the one in the next zip code over. So yeah, 9 and 10 are your best buds in this square root adventure.
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The square root of 8649 is 93
Divide the sum of the three consecutive odd integers by 3: 93 / 3 = 31. The smallest of these integers will be two less than 31 and the largest will be two more than 31, so the three consecutive odd integers will be 29, 31, and 33.
We note that sqrt(81) = 9 sqrt(100) = 10 Since 93 us between 81, & 100 , then the sqrt(93) is between '9' & '10' Since '93' is aproximately halfway between 81 & 100 we select ,say 9.5 Then 9.5 ^(2) = 90.25 ( too low Try 9.6 9.6^(2) = 92.16 ( too low , nut closer). Try 9.61 9.61^(2) = 92.3521 9.62^(2) = 92.5444 9.63^(2) = 92.7369 9.64^(2) = 92.9296 9.642^(2) = 92.9681... 9.6425^(2) = 92.9778... 9,6426^(2) = 92.979... 9.6436^(2) = 92.999,,, ~ 93 Hence the square root of '93' is 9.6436 ( 4 d.p.). NB You can keep going like this, until you arrive at the actual figure.
30 + 31 + 32 = 93 ( I forgot how to find this algebraically )
They are: 92+93+94+95 = 374