Question

PLEASE HELP!!!!!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.)

Answer 1

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

Step-by-step explanation:

The given expression is
`x=√(6) +√(7)`

Since, the perfect squares of
`2.4, 2.5, 2.6` and
`2.7` are given by

`2.4^2=5.76` ⇒
`√(5.76) =2.4`

`2.5^2=6.25` ⇒
`√(6.25) =2.5`

`2.6^2=6.76` ⇒
`√(6.76) =2.6`

`2.7^2=7.29` ⇒
`√(7.29) =2.7`

From the above perfect squares, the values close to
`√(6)` and
`√(7)` are given by

`x=√(5.76) +√(6.76)\\x =2.4+2.6\\x=5` ------------(1)

Since, the expression is
`x=√(6) +√(7)`

Substituting the values, we have,

`x=2.45+2.65\\x=5.10` -------------(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