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Math fact: The sum of any number of consecutive odd whole numbers, beginning with 1, is a perfect square e.g. 1+3=4, 1+3+5=9, =16

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**Example 1: Estimating Square Roots of Numbers**

The 55 is between two integers. Name the integers. Explain your answer. 55 36, 49, 64, 81 List perfect squares near 55. 49 < 55 < 64 Find the perfect squares nearest 55. 49 < 55 < 64 Find the square roots of the perfect squares. 7 < 55 < 8 55 is between 7 and 8 because 55 is between 49 and 64.

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**Example 2: Approximating Square Roots to the Nearest Hundredth**

Approximate √135 to the nearest hundredth. Step 1 Find the value of the whole number. 121 < 135 < 144 Find the perfect squares nearest 135. √121 < √135 < 144 √ Find the square roots of the perfect squares. 11 < 135 < 12 √ The number will be between 11 and 12. The whole number part of the answer is 11.

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Example 2 Continued Approximate √135 to the nearest hundredth. Step 2 Find the value of the decimal. Find the difference between the given number, 135, and the lower perfect square. 135 – 121 = 14 Find the difference between the greater perfect square and the lower perfect square. 144 – 121 = 23 1423 Write the difference as a ratio. Divide to find the approximate decimal value. 14 ÷ 23 ≈ 0.609

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**Approximate √135 to the nearest hundredth.**

Example 2 Continued Approximate √135 to the nearest hundredth. Step 3 Find the approximate value. Combine the whole number and decimal. = ≈ 11.61 Round to the nearest hundredth. The approximate value of to the nearest hundredth is

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**Example 3: Using a Calculator to Estimate the Value of a Square Root**

Use a calculator to find Round to the nearest tenth. 600 ≈ … Use a calculator. 600 ≈ 24.5 Round to the nearest tenth. 600 rounded to the nearest tenth is 24.5.

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