Short Cut Method to Find Squares

There are two short cut method to find squares.

Column Method
This method uses the identity (a + b)
2 = a 2 + 2ab + b 2
Step 1 : Find 572
Here a = 5 and b =7
Column I
Column II
Column III
a2
2 x a x b
b2
52= 25
2 x 5 x 7 =70
72= 49

Step II: Underline the digit of b 2 ( in column III) and add its tens digit, if any, to 2 x a x b (in column III)
Column I
Column II
Column III
a2
2 x a x b
b2
25
70 + 4 = 74
49

Step III: Underline the digit in column II and add the number formed by tens and other digit, if any, to a 2 in column I.
Column I
Column II
Column III
a2
2 x a x b
b2
25 + 7
70 + 4 = 74
49

Step IV: under the number in column I
Column I
Column II
Column III
a2
2 x a x b
b2
32
74
49

Write the underlined digits from the unit digit.
Therefore, 57
2 = 3,249 .
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Examples
1) Find the squares of the following numbers using column method: (i) 99 (ii) 89
Solution: (i) Here, a = 9 and b = 9.
We have,
Column I
Column II
Column III
a2
2 x a x b
b2
92
2 x 9 x 9
92
81
162
81
81 + 17
162 + 8 = 170
81
98
170
81
Therefore, 99 2 = 9801
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(ii) 89
2
Here, a = 8, b = 9. We have,
a2
2 x a x b
b2
82
2 x 8 x 9
92
64
144
81
64 + 15
144 + 8 = 152
81
79
152
81
:. 89 2 = 7921

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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