Answer :

(i) We have,


Cube root of -125 =


(ii) We have,


Cube root of -5832 =


So to find out the cube root of 5832, we will use the mehod of unit digits.


Let’s take number 5832.


Unit digit = 2


So unit digit in the cube root of 5832 = 8


After striking out the units, tens and hundreds digits of 5832,


Now we left with 5 only.


As we know that 1 is the Largest number whose cube is less than or equals to 5.


So,


The tens digit of the cube root of 5832 is 1.




(iii) We have,



We will use the method of factorization to find out the cube root of 2744000


Factorizing 2744000 into prime factors,


We get,


2744000 = 2×2×2×2×2×2×5×5×5×7×7×7


Now group the factors into triples of equal factors, we get,


2744000 = (2×2×2) ×(2×2×2) ×(5×5×5) ×(7×7×7)


As we can see that all the prime factors of 2744000 can be grouped in to triples of equal factors and no factor is left over.


Now take one factor from each group and by multiplying we get,


2×2×5×7 = 140


So we can say that 2744000 is a cube of 140


Hence,



(iv) We have,



By using unit digit method,


Let’s take Number = 753571


Unit digit = 1


So unit digit in the cube root of 753571 = 1


After striking out the units, tens and hundreds digits of 753571,


Now we left with 753.


As we know that 9 is the Largest number whose cube is less than or equals to 753(93<753<103).


So,


The tens digit of the cube root of 753571 is 9.




(v) We have,



By using unit digit method, we will find out the cube root of 32768,


Let’s take Number = 32768


Unit digit = 8


So unit digit in the cube root of 32768 = 2


After striking out the units, tens and hundreds digits of 32768,


Now we left with 32.


As we know that 9 is the Largest number whose cube is less than or equals to 32(33<32<43).


So,


The tens digit of the cube root of 32768 is 3.




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