Task Sets: Use rational approximations of irrational numbers - Common Core Math - Grade 8

Recall / Warm-Up

These problems review skills you already know.

Between which two consecutive whole numbers does $\sqrt{20}$ lie?

Between $4$ and $5$ , because $4^2 = 16$ and $5^2 = 25$ , and $16 < 20 < 25$ .

Between $9$ and $10$ , because $\sqrt{20}$ is about half of $20$ .

Between $19$ and $20$ , because $\sqrt{20}$ is just below $20$ .

Between $2$ and $3$ .

Which of these numbers is irrational?

$\sqrt{49}$

$\frac{3}{8}$

$\sqrt{7}$

$0.25$

Compute $1.4^2$ (the square of $1.4$ ).

Fluency Practice

Approximate, locate, compare, and estimate. Show your squaring work.

$\sqrt{5}$ lies between two consecutive tenths. Using $2.2^2 = 4.84$ and $2.3^2 = 5.29$ , what is the lower tenth (the left endpoint of the interval)?

Approximate $\sqrt{7}$ to the hundredths place by finding the lower hundredth. Test values: $2.64^2 = 6.9696$ and $2.65^2 = 7.0225$ . Give the left endpoint of the interval that traps $\sqrt{7}$ .

$Number line from 2 to 3 with tick marks labeled at every tenth, no point plotted$

On the number line shown, between which two tenths marks should $\sqrt{6}$ be placed? Use $2.4^2 = 5.76$ and $2.5^2 = 6.25$ .

Between $2.4$ and $2.5$ .

Between $2.9$ and $3.0$ .

Between $5.7$ and $6.2$ .

Exactly on $3.0$ .

Which is greater, $\sqrt{5}$ or $\sqrt{7}$ ? Use $\sqrt{5} \approx 2.24$ and $\sqrt{7} \approx 2.65$ .

$\sqrt{7}$ is greater, because $2.65 > 2.24$ and the intervals do not overlap.

$\sqrt{5}$ is greater, because $5$ comes before $7$ .

They are equal, because both round to about $2$ .

Estimate $\pi^2$ using $\pi \approx 3.14$ . Compute $3.14 \times 3.14$ and give your estimate (round to the hundredths place).

Exercises: Approximating Irrational Numbers

Recall / Warm-Up

Fluency Practice