Estimation Method For Finding Square Root

In this section we will discuss different estimation method.
There are different methods for estimating square roots.

1) Finding square roots through reducing square roots.
2) Estimation method.

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.
1² < 2 < 2²
So 256 must be 14² or 16²
As we know that 15² = 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.
6² < 38 < 7²
So 3844 must be 62² or 68²
As we know that 65² = 4225 so,
√ 3844 = 62.

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Squares and Square roots

• Introduction of Squares and Square Roots
• Perfect Squares or not
• Properties of Square Numbers
• Short cut method to find squares
• Introduction of Square Roots
• Properties of Square Roots
• Square root by Prime factorization method
• Square root by long division method
• Square root of rational numbers
• Square root of Decimals
• Square root by estimation method

From squares and square roots to Exponents

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