Question
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Estimate the square root to the nearest (a) integer and (b) tenth. \( \sqrt{46} \) a. nearest integer: \( \square \) b. nearest tenth: \( \square \)

Ask by Henry Davison. in the United States
Jan 30,2025

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Answer

a. nearest integer: 7 b. nearest tenth: 6.8

Solution

To estimate the square root of \( 46 \): ### a. Nearest Integer - \( 6^2 = 36 \) - \( 7^2 = 49 \) Since \( 46 \) is closer to \( 49 \) than to \( 36 \), the nearest integer is: **7** ### b. Nearest Tenth Calculating \( \sqrt{46} \): \[ \sqrt{46} \approx 6.7823 \] Rounding to the nearest tenth: **6.8** --- **Final Answers:** a. nearest integer: \( 7 \) b. nearest tenth: \( 6.8 \)

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To estimate \( \sqrt{46} \), we start by identifying the perfect squares around 46. Since \( 6^2 = 36 \) and \( 7^2 = 49 \), we know that \( \sqrt{46} \) lies between 6 and 7. To narrow this down further, we can check the midpoint: \( 6.5^2 = 42.25 \) (too low), and \( 6.8^2 = 46.24 \) (too high). So, the nearest integer to \( \sqrt{46} \) is 7. To find the nearest tenth, let’s refine our estimate between 6.7 and 6.8. Since \( 6.7^2 = 44.89 \) and \( 6.8^2 = 46.24 \), you can tell that \( \sqrt{46} \) is closer to 6.8. Therefore, the nearest tenth is 6.8. a. nearest integer: 7 b. nearest tenth: 6.8

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