Question

the cube root of 5832 by estimation process​

Answer 1

Answer:

5832 is the cube root of 18

Answer 2

10 cube is 1000

20 cube is 8000

So the cube root of 5832 can be 11,12,13,14,15,16,19,20.

15 cube is 3375. So it can't be 11,12,13,14,15. We are left with four choices.

We can calculate

${20}^{3} - {19}^{3}$

quite easily using

${x}^3 - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + xy)$

So

${20}^3 - {19}^3 = >$$(20 - 19)( {20}^{2} + {19}^{2} + 20 \times 19) = >$

$(400 + 361 + 380) = > 1141$

When we subtract 1141 from 8000 we get a odd number as even number - odd number is odd number. Hence 19 is not the answer. Let's find

${20}^3 - {18}^3 = >$

$(20 - 18)( {20}^{2} + {18}^{2} + 20 \times 18) = >$

$(2)(400 + 324 + 360) = > 2168$

So if we subtract 2168 from 8000 we get 5832. Hence

$\sqrt[3]{5832} = 18$

HOPE it helps you.