Square roots

key notes :

Introduction to Square Roots:

• Define what a square root is: the number that, when multiplied by itself, gives the original number.
• Example: √9 = 3 because 3 × 3 = 9.

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Perfect Squares:

• Discuss numbers like 1, 4, 9, 16, etc., which have whole numbers as square roots.
• Explore why some numbers have exact square roots (perfect squares) and others don’t.

√0	0
√1	1
√4	2
√9	3
√16	4
√25	5
√36	6
√49	7
√64	8
√81	9
√100	10
√121	11
√144	12
√169	13
√196	14
√225	15
√256	16
√289	17
√324	18
√361	19
√400	20

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Estimating Square Roots:

• Techniques for estimating square roots without a calculator.
• Example: Estimating √30 is between √25 = 5 and √36 = 6.

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Calculating Square Roots:

• Basic methods for calculating square roots manually or using a calculator.
• Step-by-step process and why it’s useful in mathematics and everyday life.

Understanding the Process:

• Definition Recap: A square root of a number x is a value y such that y² = x. For example, √16=4 because 4² = 16.

Using a Calculator:

• Basic Operation: Show students how to use the square root function on a calculator. For instance, entering 25 and pressing the square root button (√) will yield 5.
• Practice: Have students practice finding the square roots of various numbers using calculators.

Manual Methods for Finding Square Roots:

Prime Factorization Method:

• Step 1: Factor the number into its prime factors.
• Step 2: Pair the prime factors.
• Step 3: Multiply one number from each pair to get the square root.
• Example: To find the square root of 36:
  • Prime factorization: 36 = 2 × 2 × 3 × 3
  • Pairs: (2,2) and (3,3)
  • Square root: 2 × 3 = 6

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Long Division Method:

• Step 1: Pair the digits of the number from right to left (e.g., 36 becomes 36, and 144 becomes 1 44).
• Step 2: Find the largest number whose square is less than or equal to the first pair. Place this number in the quotient.
• Step 3: Subtract, bring down the next pair of digits, and repeat the process.
• Example: For √144:
  • 12 × 12 = 144, so √144 = 12.

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Square Roots in Pythagorean Theorem:

• Introduce how square roots relate to the Pythagorean Theorem (a² + b² = c²) in right triangles.
• Emphasize the importance of understanding square roots in solving problems involving triangle sides.

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Conclusion:

• Summarize the key points covered.
• Encourage students to practice calculating and estimating square roots to strengthen their skills.

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Learn with an example

Let’s Practice!