Questions: Between which two consecutive whole numbers is x² located?

Transcript text: Between which two consecutive whole numbers is $x^{2}$ located?

Solution

Solution Steps

Step 1: Understand the Problem

We need to determine between which two consecutive whole numbers the square of a point $ x $ on a number line is located. The options provided are whole numbers, and we need to find the correct range for $ x^2 $.

Step 2: Analyze the Options

The options given are:

A: 16
B: 15
C: 25
D: 20
E: 22

These represent the upper bounds of intervals between consecutive whole numbers. We need to find which interval $ x^2 $ falls into.

Step 3: Determine the Range for $ x^2 $

Since the problem does not provide the exact value of $ x $, we assume $ x $ is such that $ x^2 $ is between two consecutive whole numbers. We need to check the intervals formed by the options:

Between 15 and 16
Between 16 and 20
Between 20 and 22
Between 22 and 25

Step 4: Evaluate the Intervals

To determine the correct interval, we need to consider the possible values of $ x $ that would make $ x^2 $ fall into one of these intervals. Without the exact value of $ x $, we can only infer based on the intervals:

If $ x^2 $ is between 15 and 16, then $ x $ is approximately between $\sqrt{15}$ and $\sqrt{16}$.
If $ x^2 $ is between 16 and 20, then $ x $ is approximately between $\sqrt{16}$ and $\sqrt{20}$.
If $ x^2 $ is between 20 and 22, then $ x $ is approximately between $\sqrt{20}$ and $\sqrt{22}$.
If $ x^2 $ is between 22 and 25, then $ x $ is approximately between $\sqrt{22}$ and $\sqrt{25}$.

Final Answer

Without additional information about the exact position of $ x $ on the number line, we can only make an educated guess based on the intervals. Assuming $ x^2 $ is closest to one of the given options, the most likely interval is between 20 and 22.

\[ \boxed{\text{E 22}} \]

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