Finding square roots through reducing square roots Repeated Subtraction Method
In this method the given number is subtracted by 1,3,5,7,… at every step till you get zero at the end. The number of steps gives you the square root.
Examples
1) √49
Solution :
(i) 49 -1 = 48
(ii) 48 – 3= 45
(iii) 45 – 5 = 40
(iv) 40 – 7= 33
(v) 33 – 9 = 24
(vi) 24 – 11 = 13
(vii) 13 – 13 = 0
Here, the total number of subtractions is 7.
∴ √49 = 7
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2) √36
Solution :
(i) 36 -1 = 35
(ii) 35 – 3= 32
(iii) 32 – 5 = 27
(iv) 27 – 7= 20
(v) 20 – 9 = 11
(vi) 11 – 11 = 0
Here, the total number of subtractions is 7.
∴ √49 = 7
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Estimation method
In this method, first find the unit digit of square root from the unit digit of given number using the following table. Discard the last two digits and then check between which two squares the remaining numbers lie.
Unit digit of a given number
Unit digit of square root
1
1 or 9
4
2 or 8
5
5
6
4 or 6
9
3 or 7
Examples
1) Find the square root of 256.
Solution :
Unit digit of 256 = 6
∴ unit digit of square root = 4 or 6
Discard 56, digit remain is 2.
1^{2} < 2 < 2^{2}
So 256 must be 14^{2} or 16^{2}
As we know that 15^{2} = 225 so,
√ 256 = 16.
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2) Find the square root of 3844.
Solution :
Unit digit of 3844 = 4
∴ unit digit of square root = 2 or 8
Discard 44, digit remain is 38.
6^{2} < 38 < 7^{2}
So 3844 must be 62^{2} or 68^{2}
As we know that 65^{2} = 4225 so,
√ 3844 = 62. Squares and Square roots