SOLUTION: The question says find two consecutive whole numbers that each number falls between. Then estimate the number's value. sqrt(14) Thanks

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Question 120529: The question says find two consecutive whole numbers that each number falls between. Then estimate the number's value.

sqrt(14)

Thanks
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Look at a table of squares:


14 falls in the interval 9%3C14%3C16, therefore sqrt%2814%29 falls in the interval 3%3Csqrt%2814%29%3C4.

The difference between 9 and 16 is 7, and the difference between 9 and 14 is 5, so 14 lies 5/7ths of the way along the interval from 9 to 16, so sqrt%2814%29 should lie approximately 5/7ths of the way along the interval from 3 to 4, in other words, 3 and 5/7ths.

3 and 5/7ths, or 26/7ths rounds to 3.71. The calculator value for sqrt%2814%29 rounds to 3.74. Close enough.

Hope that helps,
John