Math Problem Statement
Solution
The image you’ve uploaded contains a table asking to classify numbers as either rational or irrational. Let’s analyze each number:
-
√6:
- The square root of 6 is not a perfect square, and its decimal form is non-terminating and non-repeating. Therefore, √6 is irrational.
-
−51/5:
- This is a fraction, and any fraction where both the numerator and denominator are integers is rational. So, −51/5 is rational.
-
√64:
- The square root of 64 is 8 (since 64 is a perfect square). Since 8 is an integer, √64 is rational.
-
9.68:
- 9.68 is a terminating decimal, and any terminating decimal is rational.
Final classification:
- √6: Irrational
- −51/5: Rational
- √64: Rational
- 9.68: Rational
Would you like more details on any of these?
Here are 5 related questions for further exploration:
- What makes a number irrational?
- Can a square root of a number ever be irrational?
- Why are terminating decimals always rational?
- What is the difference between repeating and non-repeating decimals in terms of rationality?
- Can a negative fraction ever be irrational?
Tip: A good way to remember rational numbers is that they can always be expressed as a fraction of two integers.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Number Classification
Rational Numbers
Irrational Numbers
Square Roots
Decimals
Formulas
-
Theorems
-
Suitable Grade Level
Grades 6-8
Related Recommendation
Identifying Irrational Numbers from Square Roots and Fractions
Classifying Numbers as Rational or Irrational
Classifying Rational and Irrational Numbers with Examples
Determine if a Number is Rational or Irrational for Square Roots like √81, √15
Classifying Numbers: Whole, Integer, Rational, and Irrational