Question

cube root of 0.013824​

Answer 1

cube root of 0.013824 = 0.240119346

Answer 2

Question :- find the cube root of 0.013824 . ?

Solution :-

→ 0.013824

→ (13824/1000000)

→ 13824/(100 * 100 * 100)

→ 13824/(100)³

Now, we will find cube root of 13824 by long division method .

Step 1) :-

→ 13824 = Make pairs of 3 from right . (13) - (824) . { 2 digits left after 1 pair to the left, we can keep them same or we can use 013. }

Step 2) :- Now , we have to check upto cube of which number we can go upto first pair from left.

So, upto 13 we can go to cube to 2 which is 8. { cube of 3 is 27, which will be greater than 13 .}

2) 13 - 824 (2

-8

5

Step 3) :- Now, we will take down next pair with remainder. after that, we have to find the multiplication factor for further process that comes by multiplying the first obtained digit by 30.

So,

→ MF = 2 * 30 = 60

Now, we have to find second digit . Assume second digit will be y .

Than,

→ 5824 ≥ (xy *multiplication factor + y^2) * y .

Let us take y = 4,

Than, xy = 24 . { here xy is a two digit number , which we gets by putting value of y with first quotient .}

So,

→ (24 * 60 + 4²)4

→ (1440 + 16)4

→ 1456 * 4

→ 5824 .

Therefore,

(24 * 60 + 4²)4 ) 5824 ( 24

-5824

0.

Hence, Cube root of 13824 = 24. .

So,

→ 13824/(100)³

→ (24/100)³

Than, cube root ,

→ (24/100)

→ 0.24 (Ans.)

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