Find all real square roots of 64.

Step 1:

To find the square roots of a number, determine the values that, when squared, equal the original number. 
 

Step 2:

For 64: 
\[8^ 2 = 64 \quad \text { and} \quad ( - 8) ^ 2 = 64\] 
 Step 3:

Therefore, the real square roots of 64 are \(8\) and \(- 8\).

Supplemental Knowledge:

The square root of a number is a value that, when multiplied by itself, gives the original number. For any positive real number \(x\), there are two real square roots: one positive and one negative. This is because both \(\sqrt { x} \) and \(- \sqrt { x} \) will satisfy the equation \(( \sqrt { x} ) ^ 2 = x\).

Steps to Find Square Roots: 
1. Identify the number for which you need to find the square roots. 
2. Determine both the positive and negative values that, when squared, equal the original number.

Practical Insights:

Knowledge of how to find square roots can prove useful in various fields such as.
Imagine designing a garden and needing to determine its side length on an area of 64 square meters square plot, knowing that its square root of area value (ie, +8 meters and -8 meters respectively) gives an understanding of possible configurations for such plot.

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