Basics of Square Roots
Table Of Contents
🎬 Math Angel Video: Square Roots Explained
What is a Square Root?
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🛎️ Definition of Square Root:
The square root of a number is the value that, when multiplied by itself, gives the original number.
🛎️ Examples:
- $\sqrt{9} = 3$ because $3^2 = 9$
- $\sqrt{25} = 5$ because $5^2 = 25$
Key Properties of Square Roots
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🛎️ Square roots are always non-negative.
$$ \sqrt{x} \geq 0$$
- For example: $\sqrt{9} = 3$, not $-3$
- Although $(-3)^2 = 9$, the symbol √ only represents the positive root.
🛎️ No square roots for negative numbers (in real numbers).
- For example, there’s no real number that gives $–1$ when squared.
- This means $\sqrt{-1}$ does not exist in real numbers.
How to Find Square Roots (Examples)
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Let’s practice solving square root problems step by step!
🛎️ Example 1
Question: What is $ \sqrt{1} $ ?
Answer: $ \sqrt{1} = 1 $
Because: $ 1^2 = 1 $
🛎️ Example 2
Question: What is $ \sqrt{400} $ ?
Answer: $ \sqrt{400} = 20 $
Because: $ 20^2 = 400 $
🛎️ Example 3
Question: What is $ \sqrt{144} $ ?
Answer: $ \sqrt{144} = 12 $
Because: $ 12^2 = 144 $
✅ Tip:
To find the square root of a number, ask yourself:
“What number multiplied by itself gives this number?”
List of Perfect Squares (0–15)
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It’s best to memorize these common perfect squares. They will help you find square roots much faster!
| $0^2 = 0$ | $8^2 = 64$ |
|---|---|
| $1^2 = 1$ | $9^2 = 81$ |
| $2^2 = 4$ | $10^2 = 100$ |
| $3^2 = 9$ | $11^2 = 121$ |
| $4^2 = 16$ | $12^2 = 144$ |
| $5^2 = 25$ | $13^2 = 169$ |
| $6^2 = 36$ | $14^2 = 196$ |
| $7^2 = 49$ | $15^2 = 225$ |
✅ Exam Tip:
If you remember these perfect squares, you can instantly tell that:
$ \sqrt{64} = 8 $
$ \sqrt{121} = 11 $
$ \sqrt{225} = 15 $
That’s how you get faster and more confident with square roots!
🍪 Practice: Test Your Understanding of Square Roots
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