Square Root Worksheets - Free Printable

The image you've uploaded is a Square Root Chart that lists the square roots of perfect squares from 1 to 225. Each entry shows a number and its square root, where the number is a perfect square (i.e., the product of an integer multiplied by itself).

Let’s go through the chart and explain what it means:

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🔹 What Is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number.

For example:
- $ \sqrt{4} = 2 $ because $ 2 \times 2 = 4 $
- $ \sqrt{9} = 3 $ because $ 3 \times 3 = 9 $

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🔹 Breakdown of the Chart

The chart is organized into three columns, each containing five entries:

#### ✔ Column 1: Small Perfect Squares
| Expression | Value | Explanation |
|-----------|-------|-----------|
| $ \sqrt{1} = 1 $ | 1 | $ 1 \times 1 = 1 $ |
| $ \sqrt{4} = 2 $ | 2 | $ 2 \times 2 = 4 $ |
| $ \sqrt{9} = 3 $ | 3 | $ 3 \times 3 = 9 $ |
| $ \sqrt{16} = 4 $ | 4 | $ 4 \times 4 = 16 $ |
| $ \sqrt{25} = 5 $ | 5 | $ 5 \times 5 = 25 $ |

#### ✔ Column 2: Medium Perfect Squares
| Expression | Value | Explanation |
|-----------|-------|-----------|
| $ \sqrt{36} = 6 $ | 6 | $ 6 \times 6 = 36 $ |
| $ \sqrt{49} = 7 $ | 7 | $ 7 \times 7 = 49 $ |
| $ \sqrt{64} = 8 $ | 8 | $ 8 \times 8 = 64 $ |
| $ \sqrt{81} = 9 $ | 9 | $ 9 \times 9 = 81 $ |
| $ \sqrt{100} = 10 $ | 10 | $ 10 \times 10 = 100 $ |

#### ✔ Column 3: Larger Perfect Squares
| Expression | Value | Explanation |
|-----------|-------|-----------|
| $ \sqrt{121} = 11 $ | 11 | $ 11 \times 11 = 121 $ |
| $ \sqrt{144} = 12 $ | 12 | $ 12 \times 12 = 144 $ |
| $ \sqrt{169} = 13 $ | 13 | $ 13 \times 13 = 169 $ |
| $ \sqrt{196} = 14 $ | 14 | $ 14 \times 14 = 196 $ |
| $ \sqrt{225} = 15 $ | 15 | $ 15 \times 15 = 225 $ |

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🔹 Pattern Recognition

You can see a clear pattern:
- The numbers under the square root are perfect squares: $ 1^2, 2^2, 3^2, ..., 15^2 $
- Their square roots are simply the integers from 1 to 15.

So, this chart is a helpful reference for memorizing or quickly recalling square roots of perfect squares.

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🔹 Practical Use

This chart is useful for:
- Solving algebra problems involving square roots
- Simplifying radicals
- Preparing for math tests or competitions
- Teaching students about square numbers and their roots

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🚀 Bonus Tip: Estimating Square Roots

If you need to estimate the square root of a non-perfect square (e.g., $ \sqrt{50} $), use the chart as a guide:
- $ \sqrt{49} = 7 $
- $ \sqrt{64} = 8 $
- So $ \sqrt{50} $ is between 7 and 8 — closer to 7.

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✔ Summary

This Square Root Chart displays the square roots of perfect squares from $ 1^2 $ to $ 15^2 $. It's a valuable tool for understanding and memorizing basic square roots. All values are correct and follow the rule:

> $ \sqrt{n^2} = n $ for positive integers $ n $

Let me know if you'd like help using this chart to solve a specific problem!