Introduction:
Square and square roots are mathematical concepts that are related to each other but have different meanings and calculations. Understanding the difference between them is important in order to comprehend their properties and patterns.

Difference between square and square roots:
1. Square:
- A square of a number is obtained by multiplying the number by itself.
- It is represented by the exponentiation notation, where the number is raised to the power of 2.
- For example, the square of 3 is written as 3^2 or 3 squared, which equals 9.
- The square of a number gives the area of a square with sides equal to that number.

2. Square root:
- The square root of a number is the value that, when multiplied by itself, gives the original number.
- It is denoted by the symbol √.
- For example, the square root of 9 is √9, which equals 3.
- The square root of a number gives the side length of a square with area equal to that number.

Properties of square numbers:
1. Positive values: Square numbers are always positive or zero.
2. Perfect squares: Numbers that have integer square roots are called perfect squares. Examples include 0, 1, 4, 9, 16, etc.
3. Even squares: Squares of even numbers are always even.
4. Odd squares: Squares of odd numbers are always odd.
5. Product of consecutive numbers: The square of a number is equal to the product of the number and its consecutive number. For example, 3^2 = 3 * 4 = 12.

Learning interesting patterns in square numbers:
1. Sum of consecutive odd numbers: The sum of the first n odd numbers is always equal to the square of n. For example, 1 + 3 + 5 + 7 + 9 = 25, which is equal to 5^2.
2. Sum of consecutive even numbers: The sum of the first n even numbers is equal to n multiplied by n+1. For example, 2 + 4 + 6 + 8 = 20, which is equal to 4 * 5.
3. Digit patterns: The last digit of a square number can only be 0, 1, 4, 5, 6, or 9. The last two digits of a square number can only be 00, 01, 04, 09, 16, 21, 24, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, 84, 89, or 96.
4. Pythagorean triples: Square numbers are closely related to Pythagorean triples, which are sets of three positive integers that satisfy the Pythagorean theorem (a^2 + b^2 = c^2).

Conclusion:
In summary, the difference between square and square roots lies in their calculations and meanings. Square refers to

What is the difference between square and square root? ... The square of x is the value obtained by multiplying x by itself. The square root of x is the number that, when multiplied by itself, yields x. If x = 4, its square is 16 (because 4 × 4 = 16), while its square root is ±2 (because 2 × 2 = 4 and -2 × -2 = 4).
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