Back to Use rational approximations of irrational numbers — Problem 1 · Task Set 3

8.NS.A.2 Tutor Intake -- Rational Approximations of Irrational Numbers

This short check helps your tutor see where to start. Work each problem on
your own, without a calculator. If you are not sure, give your best try —
every answer helps your tutor plan your first few sessions.

Grade 8·10 problems·~11 min·Common Core Math - Grade 8·container·8-ns-a-2

Work through problems with immediate feedback

Concepts

$1^2 = 1$ and $2^2 = 4$ . Since $1 < 2 < 4$ , what does this tell
us about $\sqrt{2}$ ?

$\sqrt{2}$ is between 1 and 2, because squaring the endpoints 1 and 2 gives values that bracket 2.

$\sqrt{2}$ equals 1.5, the number exactly halfway between 1 and 2.

$\sqrt{2}$ is between 1 and 4, matching the two squared values directly.

This tells us nothing about $\sqrt{2}$ without a calculator.