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Answer :

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.

- 1.Find the cube root of each of the following numbers by prime factorisation method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125
- 2.State True or False. (i) Cube of an odd number is even. (ii) A perfect cube does not end with two zeros. (iii) If the square of a number ends with 5, then its cube ends with 25. (iv) There is no perfect cube which ends with 8. (v) The cube of a two digit number may be a three digit number. (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number.

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- NCERT solutions for class 8 maths chapter 1 Rational Numbers
- NCERT solutions for class 8 maths chapter 1 Factorization
- NCERT solutions for class 8 maths chapter 2 Linear Equations in One Variable
- NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals
- NCERT solutions for class 8 maths chapter 4 Practical Geometry
- NCERT solutions for class 8 maths chapter 5 Data Handling
- NCERT solutions for class 8 maths chapter 6 Squares and Square Roots
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- NCERT solutions for class 8 maths chapter 8 Comparing Quantities
- NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities
- NCERT solutions for class 8 maths chapter 10 Visualising Solid Shapes
- NCERT solutions for class 8 maths chapter 11 Mensuration
- NCERT solutions for class 8 maths chapter 12 Exponents and Powers
- NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions
- NCERT solutions for class 8 maths chapter 14 Factorization
- NCERT solutions for class 8 maths chapter 15 Introduction to Graphs
- NCERT solutions for class 8 maths chapter 16 Playing with Numbers

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