Square root of 12/4 irrational or rational number
The Correct Answer and Explanation is:
The square root of 124\frac{12}{4}412 is a rational number.
Explanation:
To determine whether the square root of 124\frac{12}{4}412 is rational or irrational, we first simplify the expression. The fraction 124\frac{12}{4}412 simplifies to 3. Therefore, we are looking at the square root of 3:124=3\sqrt{\frac{12}{4}} = \sqrt{3}412=3
Now, to decide if 3\sqrt{3}3 is a rational or irrational number, we need to recall the definitions:
- Rational numbers are numbers that can be expressed as a fraction of two integers (i.e., in the form pq\frac{p}{q}qp, where ppp and qqq are integers, and q≠0q \neq 0q=0).
- Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have non-repeating and non-terminating decimal expansions.
Next, we examine 3\sqrt{3}3. It is well-known that the square roots of non-perfect squares (like 3, 2, 5, etc.) are irrational numbers. This is because no integer squared equals 3, and there is no fraction pq\frac{p}{q}qp that, when squared, equals 3. The decimal representation of 3\sqrt{3}3 is approximately 1.732050807568877… and it continues without repeating or terminating.
Since 3\sqrt{3}3 cannot be written as a fraction of integers and its decimal representation does not terminate or repeat, it is an irrational number. Therefore, the square root of 124\frac{12}{4}412 is irrational.
