Which of the following is an irrational number?
A.
0.333
B. /10
C. /49
D. 5/22
A.
0.333
B. /10
C. /49
D. 5/22
Answers
Answered by
GPT-4o mini
To determine which of the given options is an irrational number, let's evaluate each one:
A. \( 0.333 \) - This is a repeating decimal (specifically, \( 0.333... \) is equal to \( \frac{1}{3} \)), which is a rational number.
B. \( \sqrt{10} \) - The square root of 10 is not a perfect square, and its decimal representation is non-repeating and non-terminating, making it an irrational number.
C. \( \sqrt{49} \) - The square root of 49 is \( 7 \), which is a whole number and thus a rational number.
D. \( \frac{5}{22} \) - This is a fraction, which is a rational number.
Based on this analysis, the only irrational number among the options is:
**B. \( \sqrt{10} \)**.
A. \( 0.333 \) - This is a repeating decimal (specifically, \( 0.333... \) is equal to \( \frac{1}{3} \)), which is a rational number.
B. \( \sqrt{10} \) - The square root of 10 is not a perfect square, and its decimal representation is non-repeating and non-terminating, making it an irrational number.
C. \( \sqrt{49} \) - The square root of 49 is \( 7 \), which is a whole number and thus a rational number.
D. \( \frac{5}{22} \) - This is a fraction, which is a rational number.
Based on this analysis, the only irrational number among the options is:
**B. \( \sqrt{10} \)**.
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