7. 1. What is (24)2 ?
We have three approaches to find the square of any number.
1. Multiplying 24 x 24 by the Traditional method.
2. Multiplying 24 x 24 by the Criss – Cross Method.
3. Using the formula, (a + b)2 = a2 + 2ab + b2
We’ll use the 3rd approach, the Formula for calculating squares.
(24)2
Let, a = 20 and b = 4
Now, according to the formula, (a + b)2 = a2 + 2ab + b2
Therefore, (20 + 4)2 = 202 + 2(20)(4) + 42
8. (20 + 4)2 = 202 + 2(20)(4) + 42
= 400 + 160 + 16
= 560 + 16
= 576
Don’t you think, it was cumbersome and time – consuming!!!
Yes, it is!!
9. Now, let’s try this approach the Mathemagica way, using the sam
Formula:
(24)2
Answer these simple questions and we’ll derive the square of 24.
1. What is the Square of 4?
Answer is 16. We write 6 as the last digit of the answer, and
carry 1.
2. What is 2(2)(4)?
Answer is 16. We add 1 to the answer and make it 17. Now,
we write 7 as the 2nd digit of our answer and carry 1.
3. What is the square of 2?
Answer is 4. We add 1(carried) to the answer and make it 5.
We write 5 as the first digit of our answer.
10. The final answer is : 5 7 6
Let’s try a few examples:
1. (37)2
1. Square of 7 = 49 Answer
We write 9 as the last digit and carry 4. __9
2. 2(3)(7) = 42
We add, 4(carried) to the answer. i.e. 46
We write 6 as the second digit and carry 4. _69
3. Square of 3 = 9
We add 4 (carried) to the answer and make it 13.
We write 13 as the first digit of our answer. 13 6 9
Final Answer : 13 6 9
