Answer :
To determine which set contains only rational numbers, we need to examine each element in all the provided sets. A number is rational if it can be expressed as the quotient of two integers, i.e., \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\).
### Set 1: \(\{2300, 0.48, \sqrt{52}\}\)
- \(2300\) is a whole number, which is a rational number.
- \(0.48\) can be expressed as \(\frac{48}{100}\) or \(\frac{12}{25}\), which is a rational number.
- \(\sqrt{52}\) is the square root of a non-perfect square, making it an irrational number.
Since \(\sqrt{52}\) is irrational, this set contains an irrational number.
### Set 2: \(\{18, \sqrt{\pi}, \frac{12}{5}\}\)
- \(18\) is a whole number, which is a rational number.
- \(\sqrt{\pi}\) is the square root of \(\pi\), and since \(\pi\) is an irrational number, its square root is also irrational.
- \(\frac{12}{5}\) is already expressed as a fraction of two integers, making it a rational number.
Since \(\sqrt{\pi}\) is irrational, this set contains an irrational number.
### Set 3: \((0.3333\ldots, \sqrt{4}, 10)\)
- \(0.3333\ldots\) represents a repeating decimal, which can be expressed as \(\frac{1}{3}\), a rational number.
- \(\sqrt{4}\) is equal to \(2\), which is a whole number and a rational number.
- \(10\) is a whole number, which is a rational number.
This set contains only rational numbers.
### Set 4: \(\left\{\frac{3}{8}, 4, \sqrt{79}\right\}\)
- \(\frac{3}{8}\) is a fraction of two integers, making it a rational number.
- \(4\) is a whole number, which is a rational number.
- \(\sqrt{79}\) is the square root of a non-perfect square, making it an irrational number.
Since \(\sqrt{79}\) is irrational, this set contains an irrational number.
Based on this analysis, the set that contains only rational numbers is:
\((0.3333\ldots, \sqrt{4}, 10)\)
Therefore, the answer is:
[tex]\[ \boxed{3} \][/tex]
### Set 1: \(\{2300, 0.48, \sqrt{52}\}\)
- \(2300\) is a whole number, which is a rational number.
- \(0.48\) can be expressed as \(\frac{48}{100}\) or \(\frac{12}{25}\), which is a rational number.
- \(\sqrt{52}\) is the square root of a non-perfect square, making it an irrational number.
Since \(\sqrt{52}\) is irrational, this set contains an irrational number.
### Set 2: \(\{18, \sqrt{\pi}, \frac{12}{5}\}\)
- \(18\) is a whole number, which is a rational number.
- \(\sqrt{\pi}\) is the square root of \(\pi\), and since \(\pi\) is an irrational number, its square root is also irrational.
- \(\frac{12}{5}\) is already expressed as a fraction of two integers, making it a rational number.
Since \(\sqrt{\pi}\) is irrational, this set contains an irrational number.
### Set 3: \((0.3333\ldots, \sqrt{4}, 10)\)
- \(0.3333\ldots\) represents a repeating decimal, which can be expressed as \(\frac{1}{3}\), a rational number.
- \(\sqrt{4}\) is equal to \(2\), which is a whole number and a rational number.
- \(10\) is a whole number, which is a rational number.
This set contains only rational numbers.
### Set 4: \(\left\{\frac{3}{8}, 4, \sqrt{79}\right\}\)
- \(\frac{3}{8}\) is a fraction of two integers, making it a rational number.
- \(4\) is a whole number, which is a rational number.
- \(\sqrt{79}\) is the square root of a non-perfect square, making it an irrational number.
Since \(\sqrt{79}\) is irrational, this set contains an irrational number.
Based on this analysis, the set that contains only rational numbers is:
\((0.3333\ldots, \sqrt{4}, 10)\)
Therefore, the answer is:
[tex]\[ \boxed{3} \][/tex]
