Question

use the situation to answer the questions.
a function is used to calculate the side length of a square based upon the area of the square. the side length is calculated by the following formula:
$s = \sqrt{a}$, where $s$ is the side length and $a$ is the area
the formula could also be written using $x$ and $y$:
$y = \sqrt{x}$, where $y$ is the side length and $x$ is the area

1. assuming the area is measured in square meters, complete the table of values.

area ($\text{m}^2$) $x$	process $\sqrt{x}$	side length (m) $y$
1
2.25
4

Explanation:

Step1: For \( x = 0.25 \)

We use the formula \( y=\sqrt{x} \). Substitute \( x = 0.25 \) into the formula. Since \( \sqrt{0.25}=\sqrt{\frac{1}{4}} = 0.5 \), the process is \( \sqrt{0.25} \) and the side length \( y = 0.5 \).

Step2: For \( x = 1 \)

Substitute \( x = 1 \) into \( y=\sqrt{x} \). We know that \( \sqrt{1}=1 \), so the process is \( \sqrt{1} \) and the side length \( y = 1 \).

Step3: For \( x = 2.25 \)

Substitute \( x = 2.25 \) into \( y=\sqrt{x} \). Since \( \sqrt{2.25}=\sqrt{\frac{9}{4}} = 1.5 \), the process is \( \sqrt{2.25} \) and the side length \( y = 1.5 \).

Step4: For \( x = 4 \)

Substitute \( x = 4 \) into \( y=\sqrt{x} \). We have \( \sqrt{4}=2 \), so the process is \( \sqrt{4} \) and the side length \( y = 2 \).

Now we can fill the table:

Area (\( \text{m}^2 \)) \( x \)	Process \( \sqrt{x} \)	Side Length (\( \text{m} \)) \( y \)
1	\( \sqrt{1} \)	1
2.25	\( \sqrt{2.25} \)	1.5
4	\( \sqrt{4} \)	2

Answer:

The completed table is as follows:

Area (\( \text{m}^2 \)) \( x \)	Process \( \sqrt{x} \)	Side Length (\( \text{m} \)) \( y \)
1	\( \sqrt{1} \)	1
2.25	\( \sqrt{2.25} \)	1.5
4	\( \sqrt{4} \)	2