No numbers (consecutive or not) can lie between a single number.
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between which two consecutive integers does the square root lie 123
3 can't lie between consecutive whole numbers. It lies between 2 and 4, which are consecutive even numbers.
6 and 7
There are many pairs of consecutive whole numbers that lie between the square roots of 46, which are approx -6.78 and +6.78. -4 and -3, for example.
The square root of 3 will lie between 1 and 2.