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please explain with words

Let  x= sqrt6+ sqrt7 . What two consecutive integers does  x  lie between? Figure out the answer without using a calculator.

 

Explain in words how you arrived at your answer, and how you know for certain that it's correct. (Imagine that you are trying to convince a very skeptical person of this; a guess won't cut it.)

 Feb 18, 2020
 #1
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Note that    sqrt (4)  = 2   and  sqrt (9)  = 3

 

So....

 

sqrt (6) and sqrt (7)   must both  lie between   2  and 3

 

So....the  most  that   sqrt (6) + sqrt (7)  can be  is  3 + 3  =  6

 

So..... this sum must lie   between   5  and 6

 

 

cool cool cool

 Feb 18, 2020
 #2
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I don't understand why this rules out the interval 4 to 5. How does it rule out (without a calculator) 2.2 +2.7 = 4.9 for example.

 Feb 19, 2020

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