How to find Squares of Numbers ending in 5 in less than 3 seconds? : 352 452 852 etc. How to find Squares of Numbers ending in 5 in less than 3 seconds?
Lets take for example : Lets take for example 35
35 x
Here we see that : Here we see that 35
35 x That the Units place adds upto 5+5 = 10 and that the Ten’s place is same.
When this is true what we do is : When this is true what we do is 35
35 x Apply the Word Formulae ‘ By One more than the One before” to the ten’s place.
So Whats 1 more than 3?. It is 4. So we multiply 3 with 4 to get 12. That’s the first part of our answer. 12
To get the second part of our answer : To get the second part of our answer 35
35 x We multiply 5 with 5 to get 25. That’s the second part of our answer.
So our answer becomes 1225. 1225
Now try : Now try 85
85 x
Solution : Solution 85
85 x 7225 We multiply 5 with 5 to get 25. And multiply 8 with the next number 9 to get 72. So our answer becomes 7225. Simple.
Slide9 : Now try 452 552 652 952 1052 1252 etc.
in the same way.
Algebraical Proof : Algebraical Proof (10x+5)(10x+5) = 100x ( x+1) +25
Now what do we do for these sums? : Now what do we do for these sums? 26
24 x 48
42 x 67
63 x
Note that the units add upto 10 and the tens place is same. So we can apply the same rule “ By one more than the One before” . Lets see what we get. : Note that the units add upto 10 and the tens place is same. So we can apply the same rule “ By one more than the One before” . Lets see what we get. 26
24 x 48
42 x 67
63 x
In 48 x 42 we have 4 multiplied with the next number 5 which gives us 20 and 8 x2 which gives us 16. Therefore our answer 2016. Similarly try the other sums. : 26
24 x 48
42 x 67
63 x 6|24 20|16 42|21 In 48 x 42 we have 4 multiplied with the next number 5 which gives us 20 and 8 x2 which gives us 16. Therefore our answer 2016. Similarly try the other sums.