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 as illustrated below.
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
<

√18

√17
<

√19

√17
<

√20

√17
<

√21

√17
<

√22

√17
<

√23

√17
<

√24

√17
<

√25

√16
<

√17

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
<

√102

√100
<

√102

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.
May 05, 21 01:08 PM
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