QuestionAugust 24, 2025

Estimate sqrt (172) to the nearest tenth. square

Estimate sqrt (172) to the nearest tenth. square
Estimate sqrt (172) to the nearest tenth. square

Solution
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Answer

13.1 Explanation 1. Identify perfect squares around 172 12^2 = 144 and 13^2 = 169, so \sqrt{172} is between 13 and 14. 2. Calculate midpoint Midpoint between 13 and 14 is 13.5. Check if 13.5^2 is close to 172. 3. Square 13.5 13.5^2 = 182.25. This is greater than 172, so try a smaller number. 4. Square 13.1 13.1^2 = 171.61. This is very close to 172. 5. Compare with next tenth 13.2^2 = 174.24. This is further from 172 than 13.1.

Explanation

1. Identify perfect squares around 172<br /> $12^2 = 144$ and $13^2 = 169$, so $\sqrt{172}$ is between 13 and 14.<br />2. Calculate midpoint<br /> Midpoint between 13 and 14 is 13.5. Check if $13.5^2$ is close to 172.<br />3. Square 13.5<br /> $13.5^2 = 182.25$. This is greater than 172, so try a smaller number.<br />4. Square 13.1<br /> $13.1^2 = 171.61$. This is very close to 172.<br />5. Compare with next tenth<br /> $13.2^2 = 174.24$. This is further from 172 than 13.1.
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