NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS | CUBES AND CUBE ROOTS

Find here step-by-step NCERT Solutions EX 7.2 Class 8 Maths | Chapter 7 Cubes And Cube Roots from CBSE NCERT textbook.

Before moving to NCERT Solutions EX 7.2 Class 8 Maths , it is advised to go through the following topics:

• Cube And Cube Roots

NCERT Solutions EX 7.2 Class 8 Maths

Problems in Class 8 Exercise 7.2 require the knowledge of Finding Cube Roots by Factorisation Method, Estimation of Cube Roots and their applications in Word Problems.

• Finding the cube root is the inverse operation of finding cube. We know that 2^3= 8; so we say that the cube root of 8 is 2.
We write \sqrt[3]{8} = 2.

• The symbol \sqrt[3]{\,} denotes ‘cube-root.’

Exercise 7.2
Finding Cube Roots | Word Problems

QUESTION 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

ANSWER

(i) Prime facorisation of 64:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

64 = 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23

\implies \sqrt[3]{64}= \sqrt[3]{2^3\times 2^3}

\implies \sqrt[3]{64}= 2\times 2

\implies \sqrt[3]{64}= 64.

(ii) Prime facorisation of 512:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

512 = 2 × 2 × 2 × 2 × 2 × 2× 2 × 2 × 2 = 23 × 23 × 23

\implies \sqrt[3]{512}= \sqrt[3]{2^3\times 2^3\times 2^3 }

\implies \sqrt[3]{512}= 2\times 2\times 2

\implies \sqrt[3]{512}= 8.

(iii) Prime facorisation of 10648:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

10648 = 2 × 2 × 2 × 11 × 11 × 11 = 23 × 113

\implies \sqrt[3]{10648}= \sqrt[3]{2^3\times 11^3}

\implies \sqrt[3]{10648}= 2\times 11

\implies \sqrt[3]{10648}= 22.

(iv) Prime facorisation of 27000:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

27000 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5 = 23 × 33 × 53

\implies \sqrt[3]{27000}= \sqrt[3]{2^3\times 2^3}

\implies \sqrt[3]{27000}= 2\times 2

\implies \sqrt[3]{27000}= 64.

(v) Prime facorisation of 15625:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

15625 = 5 × 5 × 5 × 5 × 5 × 5 = 53 × 53

\implies \sqrt[3]{15625}= \sqrt[3]{5^3\times 5^3}

\implies \sqrt[3]{15625}= 5\times 5

\implies \sqrt[3]{15625}= 25.

(vi) Prime facorisation of 13824:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 23 × 23 × 23 × 33

\implies \sqrt[3]{13824}= \sqrt[3]{2^3\times 2^3\times 2^3\times 3^3}

\implies \sqrt[3]{13824}= 2\times 2\times 2\times 3

\implies \sqrt[3]{13824}= 24.

(vii) Prime facorisation of 110592:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 23 × 23 × 23 × 23 × 33

\implies \sqrt[3]{110592}= \sqrt[3]{2^3\times 2^3\times 2^3\times 2^3\times 3^3 }

\implies \sqrt[3]{110592}= 2\times 2\times 2\times 2\times 3

\implies \sqrt[3]{110592}= 48.

(viii) Prime facorisation of 46656:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 23 × 23 × 33 × 33

\implies \sqrt[3]{46656}= \sqrt[3]{2^3\times 2^3\times 3^3\times 3^3}

\implies \sqrt[3]{46656}= 2\times 2\times 3\times 3

\implies \sqrt[3]{46656}= 36.

(ix) Prime facorisation of 175616:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7 = 23 × 23 × 23 × 73

\implies \sqrt[3]{175616}= \sqrt[3]{2^3\times 2^3\times 2^3\times 7^3}

\implies \sqrt[3]{175616}= 2\times 2\times 2\times 7

\implies \sqrt[3]{175616}= 56.

(x) Prime facorisation of 91125:

NCERT SOLUTIONS EX 7.2 CLASS 8 MATHS

91125 = 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5 = 33 × 33 × 53

\implies \sqrt[3]{91125}= \sqrt[3]{3^3\times 3^3\times 5^3}

\implies \sqrt[3]{91125}= 3\times 3\times 5

\implies \sqrt[3]{91125}= 45.

QUESTION 2

State true or false.

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeros.

(iii) If 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.

ANSWER

(i) False,

cube of any odd number is always an odd number.

(ii) True,

if a perfect cube has zeroes at it’s end the number of zeroes must be a multiple of 3.

(iii) False,

ex- 15^2=225, 15^3=3375.

(iv) False,

2^3=8, cubes of number having 2 at units place will always end in 8 at units place.

(v) False,

smallest two digit number is 10 and 10^3 = 1000 which is a four digit number.

Therefore, cube of a two digit number will never be a three digit number.

(vi) False,

largest two digit number is 99 and 99^3 = 970299 which is a six digit number.

Therefore, cube of a two digit number will never have seven or more digits.

(vii) True,

ex- 1^3 = 1, 2^3 = 8.

QUESTION 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.

ANSWER

Making groups of three digits
starting from the right most digit of the number,

\overline{1} \,\overline{331},

We can estimate unit’s digit of the cube root from 331,

Since cube of a number having 1 at units place ends in 1, therefore unit’s digit of the required cube root will be 1,

We can estimate ten’s digit of the cube root from 1,

13 1,so ten’s digit of the required cube root will be 1,

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

Similarly,

• 4913 = \overline{4} \,\overline{913},

Unit’s digit can be estimated from {913} = 7,

Ten’s digit can be estimated from {4} as,

1^3 = 1, 2^3 = 8 and 1 < 4 < 8, so ten’s digit = 1

Thus, \sqrt[3]{4913} = 17.

• 12167 = \overline{12} \,\overline{167},

Unit’s digit can be estimated from {167} = 3,

Ten’s digit can be estimated from {12} as,

2^3 = 8, 3^3 = 27 and 8 < 12 < 27, so ten’s digit = 2,

Thus, \sqrt[3]{12167} = 23.

• 32768 = = \overline{32} \,\overline{768},

Unit’s digit can be estimated from {768} = 2,

Ten’s digit can be estimated from {32} as,

3^3 = 27, 4^3 = 64 and 27 < 32 < 64, so ten’s digit = 3,

Thus, \sqrt[3]{32768} = 32.


We hope NCERT Solutions EX 7.2 Class 8 Maths has helped you understand how to find and estimate Cube Roots of numbers and apply it to solve Word Problems.

Please write in the comment section for any error or any solution related queries from the exercise. [ NCERT Solutions EX 7.2 Class 8 Maths ]

Check NCERT Solutions of other exercises from Class 8 Maths Chapter 7 Cubes And Cube Roots by clicking the links given below.


NCERT SOLUTIONS | CLASS 8 MATHS | CHAPTER 7 | CUBES AND CUBE ROOTS

Exercise 7.1 | Exercise 7.2

Leave a Reply

Close Menu
%d bloggers like this: