# Notes for Mental Mathematics

• ## Vedic Mathematics: To Find Cube Root of a Cubic Number within Seconds

To find cube root of a cubic numbers: what are cubic numbers cube of 1= 1, (ends with 1),cube of 11= 1331 (ends with 1), and so on. cube of 2= 8, (ends with 8),cube of 12= 1728 (ends with 8), and so on. cube of 3= 27, (ends with 7),cube of 13= 2147 (ends with 7), and so on. cube of 4= 64,(ends with 8),cube of 148 (ends with 4), and so on... cube of 5= 125,(ends with 8),cube of 15 (ends with 5), and so on... cube of 6= 216,(ends with 8),cube of 16 (ends with 6), and so on... cube of 7= 343,(ends with 8),cube of 17 (ends with 3), and so on... cube of 8= 512,(ends with 8),cube of 18 (ends with 2), and so on... cube of 9= 729,(ends with 8),cube of 19 (ends with 9), and so on... cube of 10= 1000, cube of 20= 8000, cube of 30= 27000, cube of 40 = 64000, and so on. to find the cube root of a cubic number (lets take the cubic number at most of 6- digits) 1 take triplets from right. 2 decide the unit place of the cuberoot by looking at the unit place of the cube number. unit's place in the cubic number unit's place in the cubic number 1 1 2 8 3 7 4 4 5 5 6 6 7 3 8 2 9 9 ends with 3 zeros ends with one zero and so on. 3 decide the 10's place of the cuberoot by looking at the the cube number. the cubic number(x) unit's place in the cubic number 0≤x< 1000 0 1000≤x< 8000 1 8000≤x< 27000 2 27000≤x< 64000 3 64000≤x< 125000 4 125000≤x< 216000 5 216000≤x< 343000 6 343000≤x< 512000 7 512000≤x< 729000 8 729000≤x< 1000000 9 and so on. example- find cuberoot of 314432. 314432 ends with 2, so unit place of cuberoot of 314432 is 8. 216000≤314432 so cuberoot of 314432 i= 68.
Mental Mathematics
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• ## Vedic Mathematics for Finding Square of a Number whose Unit Place Carries 5

As we learned from my previous lesson i,e; (in case of two 2-digited numbers whose digits in 10's place are same and sum of the digits in unit places is 10 for example:- 38 and 32 (10's place digits are equal and 8+2=10) 38×32 can be found very easily 3×(3+1)×100=1200 (the number in 10's place × next number tio it ×100 8×2 =16 (product of digits in unit places) add the result and get the product 38×32=1200+25=1225 that's the result. we can apply it to find square of numbers ending with digit 5 35×35 = (3×4×100)+(5×5) =1225 so, square of 35=1225 practice more square of 85= 8×9×100+ 5×5 = 7200+25 =7225 is it not interesting?
Mental Mathematics
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