SOLUTION: 1. Approximate {{{sqrt(31)}}} by giving the two whole numbers that it lies between

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Question 139941: 1. Approximate sqrt%2831%29 by giving the two whole numbers that it lies between
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, note that the numbers 25 and 36 are perfect squares. In other words, 5%5E2=25 and 6%5E2=36. So since 31 is in between 25 and 36, this means that the square root of 31 is in between 5 and 6. In other words, since 25%3C31%3C36, this means 5%3Csqrt%2831%29%3C6.


Notice how 31 is 6 units away from 25 and 5 units away from 36. So 31 is about the halfway point from 25 to 36. So a good approximation for sqrt%2831%29 is 5.5 since 5.5 is halfway between 5 and 6.


So


If we take the square root of 31 with a calculator, we get sqrt%2831%29=5.5677643628. So this shows us that our approximation is very close.