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
- 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:
$$\sqrt{64} = 8$$
- 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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