To find the square roots of 36, let's start by understanding what a square root is. A square root of a number is a value that, when multiplied by itself, yields the original number.
In mathematical terms, if [tex]\( x \)[/tex] is the square root of [tex]\( y \)[/tex], then:
[tex]\[ x \times x = y \][/tex]
Here, we are looking for values of [tex]\( x \)[/tex] such that:
[tex]\[ x \times x = 36 \][/tex]
There are two values of [tex]\( x \)[/tex] that satisfy this equation: a positive value and a negative value.
First, let's consider the positive square root:
The positive square root of 36 is the value that, when multiplied by itself, results in 36. This value is 6, since:
[tex]\[ 6 \times 6 = 36 \][/tex]
Next, let's consider the negative square root:
The negative square root of 36 is the negative value that, when multiplied by itself, also results in 36. This value is -6, since:
[tex]\[ (-6) \times (-6) = 36 \][/tex]
Multiplying two negative numbers results in a positive number.
Therefore, the square roots of 36 are:
[tex]\[ 6 \text{ and } -6 \][/tex]
So, the detailed step-by-step solution to finding the square roots of 36 leads us to the values [tex]\( 6.0 \)[/tex] and [tex]\( -6.0 \)[/tex].
