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Real numbers include both rational and irrational numbers. They are numbers that appear on the number line, encompassing values like integers, fractions, and decimals. One important aspect to understand about real numbers is that they consist of positive numbers, negative numbers, and zero.
Square roots, like the one found in this exercise, fall into the category of real numbers provided the value under the square root symbol is non-negative.
If the value inside the square root symbol were negative, the result wouldn't be a real number. Instead, it would be an imaginary number. Luckily, 36 is positive, so \( \sqrt{36} \) results in a real number, which is 6.

• Rational Numbers: Numbers that can be expressed as a fraction of two integers.
• Irrational Numbers: Numbers that cannot be written as a simple fraction. This includes most square roots.

Being in this category helps us to comprehend the types of numbers we are working with, especially when determining whether a number is real or not.

The order of operations is a fundamental concept in mathematics that dictates the sequence in which we perform operations. This is often remembered by the acronym BIDMAS/BODMAS/PEDMAS:

• Brackets
• Indices (Exponents and Roots)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

In the given problem, we applied the order of operations by first calculating the square root of 36. This is because the square root (indices) operation takes precedence over applying the negative sign. Once we computed \( \sqrt{36} = 6 \), only then did we apply the negative operation to get -6. Ignore this sequence and you'll often end up with wrong answers. Understanding the correct sequence ensures accurate calculations.

Negative signs can sometimes be tricky to handle, but they are important. They indicate that a number should be taken as its additive inverse.
Applying a negative sign before a square root changes the sign of the resulting number after the root has been computed.
In this task, the square root of 36 is 6. The negative sign in front of \( \sqrt{36} \) implies that the entire expression evaluates to -6.

• Standalone Negative Signs: These are applied to a number or expression after any calculations within a grouping symbol have been completed.
• Negative Numbers: Represent values less than zero on a number line.

It's particularly important to apply their principles correctly within mathematical operations to maintain accuracy. The appropriate handling of negative signs ensures that we depict numbers accurately on the number line, in expressions, and during calculations.