Question

You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube
root? Similarly, guess the cube roots of 4913; 12167; 32768.​

Answer 1

Answer:

here your answer

Step-by-step explanation:

1331

it lies between 10^3=1000 and

20^3=8000 and it's last digit is 1

can't be the cube of 1 so

cube root of 1331 is 11

similarly

4913

it's lies between

10^3=1000 and 20^3=8000

and it's last digit 3

can't be the last digit of cube so

3√4913=17

12167

it's lies between

20^3=8000 and 30^3=270000

last digit 7

can't be the last digit of cube of but 3

so 3√12167=23

32768

u can proceed above way

u will get answer is 32

Answer 2

Solution:

We know that 10³ = 1000 and Possible cube = 11³ = 1331 Since, cube of units digit 1³ = 1.

Therefore, cube root of 1331 is 11.

4913 :--

We know that 7³ = 343

Nealy number comes with 7 as unit place 17³ = 4913. Hence, cube of 4913 is 17.

12167 :--

We know that 3² = 27

Hence, next number comes with 7 as centre place = 17³ = 2167 and next number with 3 as one's digit 23³ = 12167, Hence cube root of 121667 is 23.

32768 :--

We know that 2³ = 8

Here in cube, one's digit = 8

Now, next number with 2 as one's digit 12³ = 1728

and next number with 2 as one's digit 22³ = 10648 and next number with as one's digit 32³ = 32768.

Therefore, 32768 is 32 cube root.

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