# 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 = a2 + 2ab + b2
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 b2( 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 a2 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, 572 = 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, 992 = 9801
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(ii) 892
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
:. 892 = 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