91Ó°ÊÓ

Square roots help in simplifying certain types of algebraic expressions. The square root of a number is a value that, when multiplied by itself, gives that number. For example, the square root of 16 is 4 because 4 multiplied by 4 equals 16.
In the given exercise, we simplify the square root of 16 as follows:
\[ \sqrt{16} = 4 \]
This simplification is the first step in boiling down complex expressions to simpler forms, making calculations easier. Always look for perfect squares such as 4, 9, 16, 25, and so on when working with square roots.

Exponents are a way to express repeated multiplication of the same number. For instance, \(3^2\) means 3 multiplied by itself, which is 9. Simplifying exponents is key to streamlining algebraic expressions.
In our exercise, we needed to evaluate \(3^2\) to simplify the numerator:
\[ 3^2 = 9 \]
Knowing how to handle and simplify exponents is crucial for tackling more complicated algebraic problems efficiently.

A fraction consists of a numerator and a denominator. The numerator is the top part representing how many parts we have, while the denominator is the bottom part representing the total number of equal parts. Simplifying the numerator and denominator individually helps to manage fractions better.
For the given expression: \[ \frac{(-9+\sqrt{16})-3^2}{-6-1} \]
We first handle the numerator:
\[ -9 + \sqrt{16} - 3^2 = -9 + 4 - 9 = -14 \]
Next, we simplify the denominator:
\[ -6 - 1 = -7 \]
Finally, we combine these two simplified parts to simplify the fraction:
\[ \frac{-14}{-7} = 2 \]
Knowing how to simplify both parts separately before combining them makes the process less intimidating and more manageable.