Pregunta
whether the following statements are true or false:
The sum of two rational numbers is always a rational number.
The sum of two irrational numbers is always a rational number.
The product of two rational numbers is always a rational number.
The product of two irrational numbers is always an irrational number.
The product of two real numbers is always a real number.
When a real number is divided by a real number the result is always a real number.
The sum of a rational number and an irrational number is always an irrational numb
The product of a rational number and an irrational number is always an irrational
number. (Be careful!)
The sum of two rational numbers is always a rational number.
The sum of two irrational numbers is always a rational number.
The product of two rational numbers is always a rational number.
The product of two irrational numbers is always an irrational number.
The product of two real numbers is always a real number.
When a real number is divided by a real number the result is always a real number.
The sum of a rational number and an irrational number is always an irrational numb
The product of a rational number and an irrational number is always an irrational
number. (Be careful!)
Ask by Mullins Lowe. in South Africa
Jan 16,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
- The sum of two rational numbers is always rational: True
- The sum of two irrational numbers is always rational: False
- The product of two rational numbers is always rational: True
- The product of two irrational numbers is always irrational: False
- The product of two real numbers is always real: True
- Dividing a real number by a real number always results in a real number: True
- The sum of a rational number and an irrational number is always irrational: False
- The product of a rational number and an irrational number is always irrational: False
Solución
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The Deep Dive
The sum of two rational numbers is always a rational number. True: Adding two fractions, like 1/2 + 1/3, gives you another fraction, such as 5/6, which is also rational.
The sum of two irrational numbers is always a rational number. False: Take square roots, for example, √2 + √2 = 2√2, which is still irrational!
The product of two rational numbers is always a rational number. True: Multiplying two rational numbers like 1/2 * 3/4 results in another rational number, 3/8.
The product of two irrational numbers is always an irrational number. False: For instance, √2 * √2 = 2, a rational number.
The product of two real numbers is always a real number. True: Real numbers include both rational and irrational numbers, and their product remains in the real number set.
When a real number is divided by a real number the result is always a real number. False: Division by zero is undefined, which means an exception exists when the divisor is zero.
The sum of a rational number and an irrational number is always an irrational number. True: If you add something rational like 1 to an irrational number like √2, the result is still irrational, because no fraction can represent √2 + 1.
The product of a rational number and an irrational number is always an irrational number. True, but with a twist: If the rational number is zero, the product becomes zero, which is rational! Otherwise, it holds true.
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