Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
We need to find all real square roots of 144. A square root is a number that, when multiplied by itself, equals the original number.
Step 3:: Set Up the Equation
x^{2} = 144
This means we need to solve the equation:
Step 4:: Solve for Positive Square Root
x = 12
To find the positive square root, we take the square root of both sides:
Step 5:: Consider Negative Square Root
x = -12
Since squaring a number makes it positive, we also have a negative solution:
Step 6:: Verify Solutions
- $$(-12)^{2} = 144$$ ✓
Let's check both solutions:
Final Answer
The real square roots of 144 are 12 and - 12.
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