To estimate square roots: - Recall perfect square numbers like 4, 9, 16, 25, etc. - The square root of a number is between the greatest smaller perfect square number and the smallest greater perfect square number. - Examples show estimating the square roots of 32, 129, and 875 by identifying the closest perfect squares above and below.

1. Estimating Square Roots

2. • Recall some common perfect square numbers.
12 = 1 62 = 36 112 = 121 162 = 256
22 = 4 72 = 48 122 = 144 172 = 289
32 = 9 82 = 64 132 = 169 182 = 324
42 = 16 92 = 81 142 = 196 192 = 361
52 = 25 102 = 100 152 = 225 202 = 400

3. How to Estimate?
the greatest smaller squareroot of the smallest greater
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perfect square number a number perfect square number

4. How to estimate?
• Example: Estimate square root of 32.
• Example: Estimate square root of 129.
greater
• Example: Estimate square root of 875.

5. Example: Estimate - 40
Example: Estimate - 69
Example: Estimate - 230

6. • Example: Is 8.2 a good guess for square root of
62?
• Example: Is 11.1 a good guess for square root
of 120?

7. Example:
• Write the letter that identifies the position of
each square root.