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

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

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step-by-step explanation: