Using column method find the square of 49
Answers
Answer:
Step-by-step explanation:
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
Step-by-step explanation:
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