Square numbers - Multiplication by URBrainy.com - Free Printable

Problem Overview:

The task involves identifying and shading square numbers in a multiplication table up to 100. Square numbers are the result of multiplying a number by itself (e.g., \(1 \times 1 = 1\), \(2 \times 2 = 4\), etc.). The goal is to:

1. Shade all square numbers in the given multiplication table.
2. Write down the shaded numbers.
3. Identify the pattern in the shaded numbers.
4. Solve additional multiplication problems involving square numbers.

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Step-by-Step Solution:

#### Step 1: Shading the Square Numbers
The multiplication table provided shows products of numbers from 1 to 10. To identify square numbers, we need to shade the cells where a number is multiplied by itself. These are:

- \(1 \times 1 = 1\)
- \(2 \times 2 = 4\)
- \(3 \times 3 = 9\)
- \(4 \times 4 = 16\)
- \(5 \times 5 = 25\)
- \(6 \times 6 = 36\)
- \(7 \times 7 = 49\)
- \(8 \times 8 = 64\)
- \(9 \times 9 = 81\)
- \(10 \times 10 = 100\)

Shade these numbers in the table. The shaded numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

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#### Step 2: Writing Down the Shaded Numbers
The shaded numbers are the square numbers we identified. They are:

\[
\boxed{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
\]

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#### Step 3: Observing the Pattern
The pattern in the shaded numbers is that each number is a perfect square. Specifically:
- Each number is the result of multiplying an integer by itself.
- The sequence increases as the integers increase: \(1^2, 2^2, 3^2, \ldots, 10^2\).

This confirms that the shaded numbers are indeed square numbers.

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#### Step 4: Solving Additional Multiplication Problems
The task asks us to solve the following multiplications and confirm that the results are square numbers:

1. \(3 \times 3 = 9\)
2. \(5 \times 5 = 25\)
3. \(7 \times 7 = 49\)
4. \(9 \times 9 = 81\)
5. \(2 \times 2 = 4\)
6. \(4 \times 4 = 16\)
7. \(6 \times 6 = 36\)
8. \(8 \times 8 = 64\)

All these results are square numbers, as they are the product of a number multiplied by itself.

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Final Answer:

1. The shaded numbers are: \(\boxed{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}\).
2. The pattern is that these numbers are square numbers, formed by multiplying a number by itself.
3. The solutions to the additional multiplications are:
- \(3 \times 3 = 9\)
- \(5 \times 5 = 25\)
- \(7 \times 7 = 49\)
- \(9 \times 9 = 81\)
- \(2 \times 2 = 4\)
- \(4 \times 4 = 16\)
- \(6 \times 6 = 36\)
- \(8 \times 8 = 64\)