Which strategy can be used to locate \( \sqrt{70} \) on a number line?

To locate \( \sqrt{70} \) on a number line, you can use the **bounding integers strategy**. Here's how you can apply this method step-by-step: 1. **Identify Perfect Squares Around 70:** - Start by finding two consecutive perfect squares between which 70 lies. - \( 8^2 = 64 \) and \( 9^2 = 81 \). - Since \( 64 < 70 < 81 \), it follows that \( 8 < \sqrt{70} < 9 \). 2. **Refine the Estimate:** - To get a more precise location, determine how far 70 is from these perfect squares. - \( 70 - 64 = 6 \) and \( 81 - 70 = 11 \). - Since 70 is closer to 64, \( \sqrt{70} \) is closer to 8 than to 9. 3. **Estimate Decimal Values (Optional for Greater Precision):** - For a more accurate placement, you can estimate decimal values. - For instance, check \( 8.3^2 = 68.89 \) and \( 8.4^2 = 70.56 \). - Since \( 68.89 < 70 < 70.56 \), \( \sqrt{70} \) is between 8.3 and 8.4. 4. **Mark on the Number Line:** - Draw a number line and mark the integers 8 and 9. - Based on your estimation, place \( \sqrt{70} \) slightly above 8.3. **Visual Representation:** ``` 8 8.3 8.4 9 |-----------|------------|-----------| √70 ``` This method ensures you accurately locate \( \sqrt{70} \) by understanding its position relative to known perfect squares and refining the estimate as needed. **Summary of the Strategy:** 1. Find two consecutive integers \( n \) and \( n+1 \) such that \( n^2 < 70 < (n+1)^2 \). 2. Conclude that \( \sqrt{70} \) lies between \( n \) and \( n+1 \). 3. (Optional) Refine the estimate by considering decimal values between \( n \) and \( n+1 \). **Answer:** Use bounding integers by finding two consecutive whole numbers whose squares surround 70. Since 8² = 64 and 9² = 81, place √70 between 8 and 9 on the number line.