Pregunta
upstudy study bank question image url

Which of the following is a rational number? \[ \sqrt{62} \] \( \sqrt{96} \)\( \sqrt{16} \)

Ask by Park Davey. in the United States
Feb 28,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

√16 is a rational number.

Solución

To determine which number is rational, we need to check if each square root simplifies to a ratio of integers. 1. √62: The number 62 is not a perfect square, and it doesn't have any perfect square factors (other than 1) that allow for a complete simplification. Therefore, √62 is irrational. 2. √96: We can simplify √96 by factoring out perfect squares: √96 = √(16 × 6) = √16 × √6 = 4√6. Since √6 is irrational, 4√6 is also irrational. 3. √16: Since 16 is a perfect square, we have: √16 = 4. This is a rational number because it can be represented as 4/1. Thus, the rational number among the options is √16.

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

Beyond the Answer

Did you know that rational numbers are those that can be expressed as the quotient of two integers? For instance, \( \sqrt{16} = 4 \), which is clearly a rational number because it can be written as \( \frac{4}{1} \). On the other hand, \( \sqrt{62} \) and \( \sqrt{96} \) are not whole numbers and cannot be neatly expressed as fractions, making them irrational. In practical situations, rational numbers come in handy all the time! From budgeting your monthly expenses (like dividing the total cost of groceries among family members) to measuring ingredients in a recipe, rational numbers help keep things precise and manageable in real life. They make calculations easier and help avoid the chaos of dealing with an infinite number of decimal places!

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad