Question

24389 is a
perfect cube.
find the
unit's digit of its cube root .​

Answer 1

Answer:

9

Step-by-step explanation:

We divide the number 24389 into two parts. One is 24 and the other is 389. In the second part, the unit place of 389 is 9. Therefore it will have 9 in its cuberoot. We have to estimate the cuberoot of the first part that is 24 Therefore 8 <24 <27

3√8 < 3√24 <3√ 27

2<3√24 <3

Cuberoot of 24 lies between 2 and 3

We will take the smaller number that is 2

Therefore the number is 29

Answer 2

Question :- 24389 is a perfect cube. find the unit's digit of its cube root . ?

Solution :-

Unit digit of cubes is always independent.

Unit place of cubes :-

→ 1³ = 1 => unit place of number with 1 will always gives 1 as unit place in cube.

→ 2³ = 8 => unit place of number with 2 will always gives 8 as unit place in cube.

→ 3³ = 27 => unit place of number with 3 will always gives 7 as unit place in cube.

→ 4³ = 64 => unit place of number with 4 will always gives 4 as unit place in cube.

→ 5³ = 125 => unit place of number with 5 will always gives 5 as unit place in cube.

→ 6³ = 216 => unit place of number with 6 will always gives 6 as unit place in cube.

→ 7³ = 343 => unit place of number with 7 will always gives 3 as unit place in cube.

→ 8³ = 512 => unit place of number with 8 will always gives 2 as unit place in cube.

→ 9³ = 729 => unit place of number with 9 will always gives 9 as unit place in cube.

Now, given value is 24389 .

So,

→ Last digit of given cube 24389 = 9 => unit place of number with 9 will always gives 9 as unit place in cube.

Therefore,

→ unit digit of 24389 is 9.

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Extra :-

Now, if we want to find cube root 24389 :-

From last 3 digits we get unit digit of cube root is 9.

now, Remaining digits are 29.

So,

→ upto 24 we can go to cube of 2.

As,

→ 2³ < 24 < 3³

→ 8 < 24 < 27

Therefore,

→ Other digit of cube root = 2 .

Hence,

→ cube root of 24389 = 29 . (Ans.)

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