Math Problem Statement

Is √53 a rational number?

Solution

The question in the image asks whether 53\sqrt{53} is a rational number.

A rational number is any number that can be expressed as a fraction pq\frac{p}{q}, where pp and qq are integers and q0q \neq 0.

Since 53 is not a perfect square (its square root is not an integer), 53\sqrt{53} cannot be expressed as a fraction of two integers. Therefore, 53\sqrt{53} is not a rational number; it is an irrational number.

The correct answer to the question is "no".

Would you like further details or have any questions?

Here are 5 related questions:

  1. What is the difference between rational and irrational numbers?
  2. Can a square root ever be a rational number?
  3. How do you determine if a number is irrational?
  4. Are all square roots of prime numbers irrational?
  5. Can an irrational number be converted into a fraction?

Tip: Irrational numbers cannot be written as exact fractions, and their decimal expansions are non-repeating and non-terminating.

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Math Problem Analysis

Mathematical Concepts

Number Theory
Rational and Irrational Numbers

Formulas

A rational number can be expressed as p/q where p and q are integers, and q ≠ 0.

Theorems

Square roots of non-perfect squares are irrational.

Suitable Grade Level

Grades 6-8