📖Definition
A square root of a number is a value that, when multiplied by itself, gives the original number. The square root of 16 is 4 because 4 × 4 = 16. The symbol √ is called the radical sign.
📐Formula
If √a = b, then b × b = a. For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots: one positive and one negative, but √ typically refers to the positive root.
📝Step-by-Step Guide
Identify Perfect Squares
Check if the number is a perfect square (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...).
Simplify Non-Perfect Squares
Factor out perfect squares from under the radical.
Estimate Square Roots
For non-perfect squares, find which two perfect squares the number falls between.
Multiply and Divide Radicals
Use the rules: √a × √b = √(ab) and √a ÷ √b = √(a/b).
⚠️Common Mistakes to Avoid
- Thinking √(a + b) = √a + √b (this is wrong!)
- Forgetting that √a² = |a| (absolute value)
- Not fully simplifying radicals
- Confusing square roots with dividing by 2
- Missing the negative square root when solving equations
✏️Practice Problems
Calculate √81
Answer: 9
Simplify √48
Answer: 4√3
Simplify √75 + √27
Answer: 8√3
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