Cube & Cube-Root of any number by easy & fast way
We are applying Vedic formula for finding Cube & Cube-Root of any number by observation only. First we study the method to find cube of any number & then study to find Cube-Root of perfect cube.
Cube of number-
Vedic sutra Anurupya is applicable to find the cube of any number. As usual we will explain the steps while solving the sum. Read it 2-3 time carefully to understand the method. once you understand the method you can solve the sums in few seconds.
Ex. i) 423
Step 1: Very first step is divide the number in to two parts by slash, 4/2
Here a = 4 & b = 2
Step 2: Now find the value of first Row. If we move from right to left-
1) Left hand digit of first row is 43 = 64.
Now we move from left to right with ratio b/a i.e 2/4 = ½
2) 2nd digit in first row is = (½) x first digit
= (½) X 64 = 32
3) 3rd digit in first row is = (½ ) x Second digit
= (½) x 32 = 16
4) 4th digit in first row is = (½) x Third digit
= (½) x 16 = 08 = 23
Now our first row is, 64 32 16 8
Step 3: Second row is obtained by doubling the middle term of first row & add them.
Step 4: Now to obtained final answer we put 3 Zero behind the first term from LHS, 2 zero behind second term, one zero behind third term & no zero behind last term then add them. Adding zero rule is same for 2 & 3 digit number.
Answer, 423 = 74088
Ex. ii) 233
Step 1: Consider a =2 & b =3
Step 2:
1) Left most digit in first row is a3 = 23 = 8
2) Second digit = (b/a) x first digit
= (3/2) x 8 = 12
3) Third digit = (3/2) X 12 =18
4) Fourth digit = (3/2) x 18 = 27 = b3
Now our first row is, 8 12 18 27
Step 3: Second row is obtained by doubling the middle term of first row & add them.
Step 4: Add appropriate zero on the final row & add them.
8000 + 3600 + 540 + 27 = 12167
Answer, 233 = 12167
Similarly,
Ex.iii) 1033 = 10/3 (For 3 – digit number, LHS of slash contain 2-digit)
Here a=10 & b = 3
1) First digit of first row = 103 =1000 & ratio is b/a = 3/10
2) Second digit = (b/a) x first digit
= (3/10) x 1000 = 300
3) Third digit = (3/10) X 300 =90
4) Fourth digit = (3/10) x 90 = 9 = b3
Now our first row is, 1000 300 90 9
Step 3: Second row is obtained by doubling the middle term of first row & add them.
Now to obtained final answer add the total row by adding zero on terms,
1000000 + 90000 + 2700 + 9 =1092727
Answer, 1033 = 1092727
Cube root of perfect cube-
We will consider perfect cube only to find the cube root as practically it asked more. Initially we memorized the cube of number 1 to 10.
Now by observing the last digit of above table we make one more table
From above table we can conclude that cube of number 0,1,4,5,6 & 9 end with same number, where as cube of 2 end with 8 & cube of 3 end with 7 & vice versa.
Ex. i) Find the cube root of 85184
Step 1: Put a slash before last 3 digit
85/184
Step 2: Here last digit is 4, & we know from table 2, last digit of cube is 4, So last digit of cube root will be also 4.
So, we get our last digit _4.
Step 3: To find first digit of the answer, we observe LHS of the given cube. It is 85 here. 85 lies between –
Step 4: Out of these two number 4 & 5 we take smaller number as first digit of our answer. (Always take smaller number from two)
So, our first digit is 4.
Answer, cube root of 85184 = 44.
Ex. ii) Find the cube root of 1728
Step 1: 1/728
Step 2: Last digit of answer = _2 (From table 2)
Step 3: LHS part of slash is 1, which is cube root of 1
Step 4: So, our first digit = 1.
Answer, cube root of 1728 = 12.
Ex. iii) Find the cube root of 681472.
Step 1: 681/472
Step 2: Last digit of Answer = _8 (From table 2)
Step 3: 681 lies between 512 & 729, which are the cube of 8 &9
Step 4: From 8 & 9 smaller number is 8, So our first digit is 8.
Answer, cube root of 681472 = 88
Ex. iv) Ex. iii) Find the cube root of 1225043
Step 1: 1225/043
Step 2: Last digit of Answer = _7 (From table 2)
Step 3: 1225 lies between 1000 & 1331, which are the cube of 10 & 11.
Step 4: From 10 & 11 smaller number is 10, So our first digit is 10.
Answer, cube root of 1225043 = 107.
Find this Link to Study more:
1.Find the square & Square-root of any number by observation only
2.Base Method of Multiplication: Multiply a number near the base in 3-4 seconds
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