Is the square root of 2 and 3 a rational number or irrational?
Understand the Problem
The question is asking whether the square roots of 2 and 3 are rational or irrational numbers. A rational number can be expressed as the quotient of two integers, while an irrational number cannot.
Answer
The square roots of 2 and 3 are both irrational numbers.
The square roots of 2 and 3 are both irrational numbers.
Answer for screen readers
The square roots of 2 and 3 are both irrational numbers.
More Information
A rational number can be expressed as the quotient of two integers, whereas an irrational number cannot. Since 2 and 3 are not perfect squares, their square roots cannot be expressed as a simple fraction, making them irrational.
Tips
A common mistake is assuming that square roots of non-perfect squares like 2 and 3 are rational if they appear in a simple form, which is incorrect. Always check if the number under the root is a perfect square.
Sources
- Identifying Rational and Irrational Numbers - Lumen Learning - courses.lumenlearning.com
- Prove that sqrt(2) + sqrt(3) Cannot be a Rational Number - YouTube - youtube.com
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