Question

(a) plot $4 - \sqrt{5}$ and $\sqrt3{2}$ on the decimal number line.
note that you can use the calculator.
number line from 1 to 2 with ticks at 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2

(b) based on your answer above, compare $4 - \sqrt{5}$ and $\sqrt3{2}$ using $<$, $>$, or $=$.
$4 - \sqrt{5} \square \sqrt3{2}$
options: $\square<\square$, $\square>\square$, $\square=\square$

Explanation:

Part (a)

Step 1: Calculate \( 4 - \sqrt{5} \)

First, find the value of \( \sqrt{5} \approx 2.236 \). Then, \( 4 - \sqrt{5} \approx 4 - 2.236 = 1.764 \).

Step 2: Calculate \( \sqrt[3]{2} \)

Using a calculator, \( \sqrt[3]{2} \approx 1.260 \).

Step 3: Plot on the number line

• For \( 4 - \sqrt{5} \approx 1.764 \), it is between 1.7 and 1.8, closer to 1.8.
• For \( \sqrt[3]{2} \approx 1.260 \), it is between 1.2 and 1.3, closer to 1.3.

Part (b)

Compare the decimal values we found: \( 4 - \sqrt{5} \approx 1.764 \) and \( \sqrt[3]{2} \approx 1.260 \). Since \( 1.764 > 1.260 \), we can determine the relationship.

Answer:

(a):

• \( 4 - \sqrt{5} \approx 1.764 \) is plotted near 1.7 - 1.8.
• \( \sqrt[3]{2} \approx 1.260 \) is plotted near 1.2 - 1.3.