Relationship between squares and square roots

key notes:

1. Definition of Square Numbers:

• A square number is the result of multiplying an integer by itself.
• The square of a number nnn is written as n².

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2. Definition of Square Roots:

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

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3. Relationship between Squares and Square Roots:

• A square root is the reverse of squaring a number.

• In other words, squaring a number gives a square number, and taking the square root of a square number gives the original number.

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4. Properties of Square Numbers and Square Roots:

• Perfect Squares: Only perfect squares (numbers like 1, 4, 9, 16, 25) have integer square roots.
• Non-perfect Squares: Numbers that are not perfect squares (such as 2, 3, 5, 7) have irrational square roots.

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5. Square and Square Root Example:

• This shows the reverse relationship: squaring gives 36, and taking the square root of 36 returns 6.

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6. Principles of Using Square Roots:

• The square root of a product is the product of the square roots:

• The square root of a quotient is the quotient of the square roots:

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7. Negative Numbers:

• The square root of a negative number is not a real number. It is defined as an imaginary number (denoted as iii).

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