Use the calculator below to approximate √114 as a decimal to the hundredths place. Note that you must do...

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Use the calculator below to approximate √114 as a decimal to the hundredths place.
Note that you must do the approximation without using a square root button. Your answer must be within a hundredth of the actual value.

SnapAndSolve AI · Accepted Answer

To approximate √114 to the hundredths place without using a square root button, you can use the method of successive approximations: Estimate a starting point. Since 10² = 100 and 11² = 121, √114 is between 10 and 11. Try 10.5: 10.5² = 110.25, which is less than 114. Try 10.6: 10.6² = 112.36, which is less than 114. Try 10.7: 10.7² = 114.49, which is more than 114. Since 10.6² is less than 114 and 10.7² is more, try a number between them, like 10.65: 10.65² = 113.4225, which is less than 114. Try 10.66: 10.66² = 113.6356, which is less than 114. Try 10.67: 10.67² = 113.8489, which is less than 114. Try 10.68: 10.68² = 114.0624, which is more than 114. Therefore, √114 is approximately 10.67 to the hundredths place.

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Use the calculator below to approximate √114 as a decimal to the hundredths place. Note that you must do...

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