ESTIMATE SQUARE ROOTS
When we estimate the square root of a number, first we will find the two values between which the square root of the given number lies.
For example square root of the number 40 lies between 6 and 7.
Because square root of 36 is 6 and square root of 49 is 7. The given number lies between 36 and 49. So that we can say that the square root of the given number is between 6 and 7.
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
√169 = 13
√196 = 14
√225 = 15
√256 = 16
√289 = 17
√324 = 18
√361 = 19
√400 = 20
√441 = 21
√484 = 22
√529 = 23
√576 = 24
√625 = 25
√676 = 26
√729 = 27
√784 = 28
√841 = 29
√900 = 30
From the above square roots, we can come to know that
(i) If a perfect square has ‘n’ digits where n is even, its square root has n/2 digits.
(ii) If a perfect square has ‘n’ digits where n is odd, its square root has (n + 1)/2 digits.
Example 1 :
Estimate the value of the following to the nearest whole number.
√80
Solution :
√64 < √80 < √81
8 < √80 < 9
Since the given number lies between 64 and 81, the approximate square root of the given number is 8.
So, the approximate value of √80 is 8.
Example 2 :
Estimate the value of the following to the nearest whole number.
√1000
Solution :
The given number is greater than 900. If we multiply 32 x 32 we will get 1024 which is greater than 1000. So we have to try the number less than 32 but greater than 30.
31 x 31 = 961 < 1000
So, the approximate value of √1000 is 31.
Example 3 :
Estimate the value of the following to the nearest whole number.
√172
Solution :
The given number is greater than 169 and lesser than 196. So the square root of the given number lies between 16 and 17.
So, the approximate value of √172 is 16.
Example 4 :
Estimate the value of the following to the nearest whole number.
√5928
Solution :
Number of digits in the given number = 4
So, square root of 5928 will have 2 digits.
70 x 70 = 4900
75 x 75 = 5625
77 x 77 = 5929
So, the approximate value √5928 is 76.
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