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

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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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