# Topics for this presentation are 1. Astronomical multiplication 2. Cube root 3. Square root,etc Done by L.Hariharan.

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Topics for this presentation are 1. Astronomical multiplication 2. Cube root 3. Square root,etc Done by L.Hariharan

Aim: To multiply 9999999993 *9999999994 Don’t try it in your calculator it will give you only an approximate value. Let us do it now mentally. We will try to understand it with simple example 95 +5 { Nearest + or - to give 100,1000,etc} * 92 +8 87 40 { 92-5 = 87 or 95-8 = 87 } and 8*5=40 Answer is 8740

Similarly answer for astronomical multiplication is 99999999870000000042 ANSWER Now let us go to find cube roots

Finding cube root requires some background

Examples : 9,261 1,728 32,768 175,616 Solution for 32,768 By seeing last digit we find last digit of cube root is equal to 2. (refer previous slide) By seeing 32 we put 3, as our first digit as 3 3 = 27 is less than 32 and 4 3 = 64 is more. Our answer is 32.

What is the square root of the number given below? 123456787654321 a) 1234569 b) 23456791 c) 11111111 d) 1267541 Note : Expected time to solve the problem is 5 to 10 seconds

First of all the pattern: Square of 1 = 1 Square of 11 = 121 Square of 111 = 12321 Square of 1111 = 1234321 Square of 11111 = 123454321 Square of 111111 = 12345654321 Square of 1111111 = 1234567654321 And so on and so forth. Answer choice is c

Note: No.s are arranged in knight movement as in the chess game. The sum is 260.