One way to estimate the square root of any number is to find a whole number greater than the square root and another whole number less than the square root.
Take a close look at the figure below so you can learn the process.
There is a very important observation you need to make!
In our example above, notice that 34 is much closer to 36 than it is to 25.
Therefore, we chose a number very close to 6 and that number is 5.8.
We will illustrate the process with two more examples.
Example #1:
Estimate the square root of 17
We will find a whole number bigger than the square root of 17 and a whole number smaller than the square root of 17.
√17
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√18
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√17
<
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√19
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√17
<
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√20
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√17
<
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√21
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√17
<
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√22
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√17
<
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√23
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√17
<
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√24
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√17
<
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√25
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√16
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√17
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Example #2:
Estimate the square root of 102
We will find a whole number bigger than the square root of 102 and a whole number smaller than the square root of 102.
√101
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√102
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√100
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√102
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Notice that the square root of any number between 103 and 120 is not a whole number.
However, square root of 121 is a whole number since 11 times 11 = 121.
Therefore, the square of 121 will give us the whole number that we need that is bigger than square of 102.
Notice again that in our estimation, we chose a number close to 10 since 102 is much closer 100 than it is 121.
Jan 26, 23 11:44 AM
Jan 25, 23 05:54 AM