Question

practice & problem solving

1. leveled practice find the rational approximation of $sqrt{15}$.

a. approximate using perfect squares.
$square < 15 < square$
$square < sqrt{15} < square$
$square < sqrt{15} < square$
b. locate and plot $sqrt{15}$ on a number line.
find a better approximation using decimals.
$3.8 \times 3.8 = square$
$3.9 \times 3.9 = square$
(number line with markings from 3 to 4, with increments of 0.1)

1. compare $-1.96, 3.12\dots$ and $-sqrt{5}$.

show your work.

1. does $\frac{1}{4}, -3, \sqrt{7}, -\frac{5}{2}$, or 4.5 come first when the numbers are listed from least to greatest? explain.
2. a museum director wants to hang the painting on a wall. to the nearest foot, how tall does the wall need to be?

(image of a painting with height marked as $sqrt{90}$ ft)

1. dina has several small clay pots. she wants to display them in order of height, from shortest to tallest. what will be the order of the pots?

(images of four pots with heights marked as $sqrt{8}$ in, $2\frac{1}{3}$ in, $sqrt{5}$ in, 2.5 in)

Explanation:

Step1: Q8a: Find surrounding perfect squares

$16 < 18 < 25$
Take square roots:
$\sqrt{16} < \sqrt{18} < \sqrt{25}$
$4 < \sqrt{18} < 5$

Step2: Q8b: Calculate decimal products

$3.8 \times 3.8 = 14.44$
$3.9 \times 3.9 = 15.21$
(Note: $\sqrt{18} \approx 4.24$, so it plots between 4.2 and 4.3 on the number line)

Step3: Q9: Approximate $-\sqrt{5}$

$\sqrt{5} \approx 2.236$, so $-\sqrt{5} \approx -2.236$
Compare: $-2.236 < -1.96 < 1.2$

Step4: Q10: Convert all to decimals

$\frac{1}{2}=0.5$, $-3$, $\sqrt{7}\approx2.646$, $-\frac{3}{4}=-0.75$, $4.5$
Order from least: $-3 < -0.75 < 0.5 < 2.646 < 4.5$

Step5: Q11: Approximate $\sqrt{90}$

$\sqrt{81}=9$, $\sqrt{100}=10$, $\sqrt{90}\approx9.49$, rounded to 9 ft

Step6: Q12: Convert all heights to decimals

$\sqrt{5}\approx2.236$ in, $2.5$ in, $2\frac{1}{3}\approx2.667$ in, $\sqrt{8}\approx2.828$ in
Order shortest to tallest: $\sqrt{5} < 2.5 < 2\frac{1}{3} < \sqrt{8}$

Answer:

8a. $4 < \sqrt{18} < 5$
8b. $3.8 \times 3.8 = 14.44$; $3.9 \times 3.9 = 15.21$; $\sqrt{18}$ plots between 4.2 and 4.3 on the number line

1. $-\sqrt{5} < -1.96 < 1.2$
2. $-3$ comes first. When converted to decimals, $-3$ is the smallest value.
3. 9 feet
4. $\sqrt{5}$ in pot, 2.5 in pot, $2\frac{1}{3}$ in pot, $\sqrt{8}$ in pot (from shortest to tallest)