DUE TOMORROW
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.)

The two consecutive integers that x lies between is 5 and 6

Explanation:

The given expression is

Since, the perfect squares of and are given by

⇒

⇒

⇒

⇒

From the above perfect squares, the values close to and are given by

------------(1)

Since, the expression is

Substituting the values, we have,

       -------------(2)

Thus, from (1) and (2), the values of x lies between 5 and 6

Hence, the two consecutive integers that x lies between is 5 and 6

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step-by-step explanati∵∵∴∴on:

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values