PARAM Mathematics Classes'

If the two numbers differ by 6 then their product is the square of their average minus 9.
Let me explain this rule by taking examples
10*16 = 13^2 - 9 = 160
22*28 = 25^2 - 9 = 616 

Shortcut to find the square root

square root x

This trick will help you to find the square roots using shortcut. Learn the shortcut with the simplified steps given below.

We have to remember the ending digit of the square of numbers from 1 to 9. i,e square root of 9 is 81. So it ends with 1. Square of 8 is 64, so it ends with 4.

Step 1: Divide the numbers in pairs of two, starting from right side. For example lets us consider

1156, which can be split as 11 and 56

Step 2: From the first part (i.e 11) find the nearest square number.

Nearest square number below 11 is 9. Square root of the square 9 is 3. So the 1st part of the answer is 3.

Step 3: Now lets take the second part (i.e 56) and see the ending number. Its 6. Use that number to find the square root number from the table above.

For 6 we can either get 4 or 6

Step 4: From the above steps we can conclude that the square root will be either 34 or 36. 3 derived from first part in step 3. 4 or 6 derived from second part in step 6.

1729 is the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see the Indian mathematician Srinivasa Ramanujan. In Hardy's words:[1][2][3][4]

“ I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247
Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it. This is the method of multiplying any two digit no from 11 to19

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