The Total solution for NCERT class 6-12
The given perfect cube =1331Forming groups of three from the rightmost digits of 1331IInd group = 11st group = 331One’s digit in first group = 1One’s digit in the required cube root may be 1.The second group has only 1.Estimated cube root of 1331 = 11Thus =11(i) Given perfect cube = 4913Forming groups of three from the right most digit of 4913IInd group = 41st group = 913One’s place digit in 913 is 3.One’s place digit in the cube root of the given number may be 7.Now in IInd group digit is 413 < 4 < 23Ten’s place must be the smallest number 1.Thus, the estimated cube root of 4913 = 17.(ii) Given perfect cube = 12167Forming group of three from the rightmost digits of 12167We have IInd group = 121st group = 167The ones place digit in 167 is 7.One’s place digit in the cube root of the given number may be 3.Now in Ilnd group, we have 1223 < 12 < 33Ten’s place of the required cube root of the given number = 2.Thus, the estimated cube root of 12167 = 23.(iii) Given perfect cube = 32768Forming groups of three from the rightmost digits of 32768, we haveIInd group = 321st group = 768One’s place digit in 768 is 8.One’s place digit in the cube root of the given number may be 2.Now in IInd group, we have 3233 < 32 < 43Ten’s place of the cube root of the given number = 3.Thus, the estimated cube root of 32768 = 32.