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 57^{2}
Here a = 5 and b =7


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)


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.







Step IV: under the number in column I


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,













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(ii) 89 ^{2}
Here, a = 8, b = 9. We have,












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
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