3.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.

We have the perfect cube = 1331
Now let us form groups of three from the rightmost digits of 133

So we have,

Group 2= 1 and, group 1= 331

One’s digit in first group = 1, that says that one’s digit in the required cube root may be 1.Also, in the second group we have only 1.

Estimated cube root of 1331 = 11

Thus, \(\sqrt [ 3 ]{ 1331 } = 11\)

(i) We have the perfect cube = 4913

Now let us form groups of three from the rightmost digits of 4913

So we have,

group 2 = 4 And,group 1= 913

One’s place digit in 913 is 3.So that says that one’s place digit in the cube root of the given number may be 7.

Now in group 2 digit is 4 and we know that 4 lies as:\(1^3 < 4 < 2^3\).We know that, ten’s place must be the smallest number i.e,1.

Thus, the estimated cube root of 4913 = 17.

(ii) We have the perfect cube = 12167

Now let us form groups of three from the rightmost digits of 12167

So we have,

group 2= 12 and, group 1= 167

The ones place digit in 167 is 7.So we can say that one’s digit in the cube root of the given number may be 3.

Now in group 2, we have 12 and 12 lies between as:\(2^3 < 12 < 3^3\). Also, we know that the ten’s place of the required cube root of the given number = 2

. Thus, the estimated cube root of 12167 = 23.

(iii) We have the perfect cube = 32768

Now let us form groups of three from the rightmost digits of 32768, we have

So we have,

group 2= 32 and, group 1= 768

One’s place digit in 768 is 8.So we can say that the one’s place digit in the cube root of the given number may be 2.

Now in group 2, we have 32 and 32 lies between the numbers as:\(3^3 < 32 < 4^3\).Also, we know that the ten’s place of the cube root of the given number = 3.

Thus, the estimated cube root of 32768 = 32.