As a mathematics expert, I have a deep understanding of the properties of numbers, including rational and irrational numbers. Rational numbers are those that can be expressed as the quotient or fraction \[p/q\] where \(p\) and \(q\) are integers and \(q \neq 0\). Irrational numbers, on the other hand, cannot be expressed as a simple fraction; they are non-repeating, non-terminating decimals.

Now, let's address the question at hand: Is the square root of 36 rational or irrational? The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, if \( x \) is a number, then \( \sqrt{x} \) is the square root of \( x \) such that \( (\sqrt{x})^2 = x \).

To determine if the square root of 36 is rational or irrational, we need to find a number \( y \) such that \( y^2 = 36 \). When we perform the calculation, we find that \( 6^2 = 36 \). Since 6 is an integer, it can be expressed as a fraction \( 6/1 \), which fits the definition of a rational number.

It's important to note that not all square roots result in rational numbers. For example, the square root of 5 cannot be expressed as a fraction of two integers because there is no integer that can be multiplied by itself to yield 5. This is a characteristic of irrational numbers. However, in the case of the square root of 36, we have a perfect square, and thus the result is a rational number.

In summary, the square root of 36 is a rational number because it can be expressed as an integer, and that integer can also be expressed as a fraction with a denominator of 1. This is a key distinction between rational and irrational numbers, and it's crucial for understanding the properties of numbers in mathematics.

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Since there is no integer that can be multiplied by itself to make 5, the square root of 5 is irrational. (T/F): The square root of 36 is an irrational number. False. EXPLANATION: The square root of 36 is 6, which is an integer, and therefore rational.read more >>