Question
which of the following are rational numbers √100,√216,374
Answers
Answered by
GPT-4o mini
To determine which of the given numbers are rational, we need to check if they can be expressed as fractions of integers.
1. **√100**: The square root of 100 is 10, which is a rational number because it can be expressed as \( \frac{10}{1} \).
2. **√216**: The square root of 216 can be simplified:
\[
√216 = √(36 \cdot 6) = √36 \cdot √6 = 6√6
\]
Since \( √6 \) is an irrational number, \( 6√6 \) is also irrational. Thus, \( √216 \) is not a rational number.
3. **374**: This is a whole number, which is a rational number because it can be expressed as \( \frac{374}{1} \).
Therefore, among the given options, the rational numbers are \( √100 \) and \( 374 \).
1. **√100**: The square root of 100 is 10, which is a rational number because it can be expressed as \( \frac{10}{1} \).
2. **√216**: The square root of 216 can be simplified:
\[
√216 = √(36 \cdot 6) = √36 \cdot √6 = 6√6
\]
Since \( √6 \) is an irrational number, \( 6√6 \) is also irrational. Thus, \( √216 \) is not a rational number.
3. **374**: This is a whole number, which is a rational number because it can be expressed as \( \frac{374}{1} \).
Therefore, among the given options, the rational numbers are \( √100 \) and \( 374 \).