Is the square root of 64 rational or irrational?

Understand the Problem

The question is asking whether the square root of 64 is a rational number or not. A rational number is a number that can be expressed as a fraction of two integers, while an irrational number cannot be expressed in such a way. To solve this, we will find the square root of 64 and determine its classification.

Answer

Yes, the square root of 64 is a rational number.
Answer for screen readers

Yes, the square root of 64 is a rational number.

Steps to Solve

  1. Find the square root of 64

To determine if the square root of 64 is a rational number, we first need to compute the square root.

The square root of 64 is calculated as follows:

$$\sqrt{64} = 8$$

  1. Determine if 8 is a rational number

Next, we need to classify the number 8. A rational number can be expressed as a fraction of two integers. The number 8 can be written as:

$$\frac{8}{1}$$

Since both 8 and 1 are integers, it confirms that 8 is indeed a rational number.

Yes, the square root of 64 is a rational number.

More Information

The square root of 64 is a whole number, specifically 8. Whole numbers are always considered rational numbers as they can be expressed as fractions (like $\frac{8}{1}$), fulfilling the criteria for rationality.

Tips

  • Confusing square roots of perfect squares: Some may think that the square root of a number can only be irrational, but perfect squares like 64 yield integer results which are rational.
  • Misunderstanding rational numbers: It's important to remember that all integers (positive, negative, and zero) are rational because they can be expressed as fractions.

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