Question
Is the square root of 49 a rational or irrational and a repeating non-repeating or neither
Answers
Answer
Is it terminating?
Answered by
GPT-4o mini
The square root of 49 is 7, since \( 7 \times 7 = 49 \). Since 7 is an integer, it is also a rational number.
To clarify the types of numbers:
- **Rational numbers** are numbers that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- **Irrational numbers** cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions.
- **Repeating decimals** are a subset of rational numbers that have a decimal representation that eventually falls into a repeating pattern.
In this case, since 7 is a whole number, it is a rational number and can also be expressed as a non-repeating decimal (7.0). So the square root of 49 is rational and non-repeating.
To clarify the types of numbers:
- **Rational numbers** are numbers that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- **Irrational numbers** cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions.
- **Repeating decimals** are a subset of rational numbers that have a decimal representation that eventually falls into a repeating pattern.
In this case, since 7 is a whole number, it is a rational number and can also be expressed as a non-repeating decimal (7.0). So the square root of 49 is rational and non-repeating.
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