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What is the square root of 184?

Updated: 4/28/2022
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7y ago

Best Answer

13.56465997

or 2 radical 46

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7y ago
This answer is:
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11y ago

13.5647 (rounded)

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Q: What is the square root of 184?
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What is the Estimate the square root of 184 by finding the consecutive whole numbers it lies between?

132 = 169 < 184 < 196 = 142 So 13 < √184 < 14 So estimating from consecutive whole numbers would give the answer "13 and a bit". But you can do better than that by interpolating. The square-root function is, obviously, not linear but you will not go too far wrong between consecutive integers (unless you are dealing with very small number). 184 is (184-169)/(196-169) = 15/27 of the distance between 132 and 142 so the square root is approx 15/27 = 5/9 of the way from 13 to 14 ie 13+5/9 = 13.555... recurring. In fact, the correct value is approx 13.5647 so the estimate is accurate to 2 decimal places.