8.NS Tutor Intake — Irrational Numbers and Rational Approximation

A number is rational if it can be written as a ratio
$\frac{p}{q}$ of two integers with $q \neq 0$, and irrational
if it cannot. Some square roots are rational and some are not.
Evaluate $\sqrt{16}$, the one square root among
$\sqrt{16}, \sqrt{15}, \sqrt{14}$ that is a rational number. Enter
your answer as a whole number.

Every real number has a decimal expansion. A rational number's
expansion terminates or eventually repeats; an irrational number's
expansion is infinite and never repeats. Which of the following
decimal expansions belongs to an irrational number?

When you convert a fraction $\frac{p}{q}$ to a decimal by long
division, the decimal eventually repeats. For a fraction with
denominator $11$, what is the longest a repeating block could
possibly be?

Convert the repeating decimal $0.\overline{4}$ (that is,
$0.4444\ldots$) to a fraction in simplest form. Enter your answer
as a fraction.

You are approximating $\sqrt{7}$ by squaring candidate values.
You find that $2.6^2 = 6.76$ and $2.7^2 = 7.29$. Between which two
consecutive tenths does $\sqrt{7}$ lie? Enter the smaller (lower)
bound as a decimal.

Use rational approximations to compare $\sqrt{10}$ and $\pi$.
You may use $\pi \approx 3.14159$. Which statement is true?