Questions: Which of the following is a rational number? The square root of 9 The square root of 2 The square root of 20 The square root of 15

Which of the following is a rational number? The square root of 9 The square root of 2 The square root of 20 The square root of 15
Transcript text: Which of the following is a rational number? The square root of 9 The square root of 2 The square root of 20 The square root of 15
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Solution

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Solution Steps

To determine which of the given options is a rational number, we need to check if the square root of each number is a whole number. A rational number can be expressed as a fraction of two integers, and whole numbers are a subset of rational numbers. Therefore, we will calculate the square root of each number and check if it is an integer.

Step 1: Identify the Nature of Each Square Root

To determine which of the given numbers has a rational square root, we calculate the square root of each number: \( \sqrt{9} \), \( \sqrt{2} \), \( \sqrt{20} \), and \( \sqrt{15} \).

Step 2: Calculate the Square Roots
  • \( \sqrt{9} = 3 \)
  • \( \sqrt{2} \approx 1.414 \)
  • \( \sqrt{20} \approx 4.472 \)
  • \( \sqrt{15} \approx 3.873 \)
Step 3: Determine Rationality

A number is rational if it can be expressed as a fraction of two integers. In this context, a square root is rational if it results in a whole number. From the calculations:

  • \( \sqrt{9} = 3 \) is a whole number.
  • \( \sqrt{2} \), \( \sqrt{20} \), and \( \sqrt{15} \) are not whole numbers.

Final Answer

\(\boxed{\sqrt{9}}\)

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