NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 7 |

Chapter Name |
Cubes and Cube Roots |

Exercise |
Ex 7.2 |

Number of Questions Solved |
3 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.2

**Ex 7.2 Class 8 Maths 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

**Solution:**

**(i)** Resolving 64 into prime factors, we get

64 = 2 x 2 x 2 x 2 x 2 x 2

∴ \(\sqrt [ 3 ]{ 64 } =\left( 2\times 2 \right) =4\)

**(ii)** Resolving 512 into prime factors, we get

512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

∴ \(\sqrt [ 3 ]{ 512 } =\left( 2\times 2\times 2 \right) =8\)

**(iii)** Resolving 10648 into prime factors, we get

10648 = 2 x 2 x 2 x 11 x 11 x 11

∴ \(\sqrt [ 3 ]{ 10648 } =\left( 2\times 11 \right) =22\)

**(iv)** Resolving 27000 into prime factors, we get

27000 = 1000 x 27

= 10 x 10 x 10 x 3 x 3 x 3 = 2 x 5 x 2 x 5 x 2 x 5 x 3 x 3 x 3

= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

∴ \(\sqrt [ 3 ]{ 27000 } =2\times 3\times 5=30\)

**(v)** Resolving 15625 into prime factors, we get

15625 = 5 x 5 x 5 x 5 x 5 x5

∴ \(\sqrt [ 3 ]{ 15625 } =5\times 5=25\)

**(vi) **Resolving 13824 into prime factors, we get

13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

∴ \(\sqrt [ 3 ]{ 13824 } =\left( 2\times 2\times 2\times 3 \right) =24\)

**(vii)** Resolving 110592 in prime factors, we get

110592 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

∴ \(\sqrt [ 3 ]{ 110592 } =\left( 2\times 2\times 2\times 2\times 3 \right) =48\)

**(viii)** Resolving 46656 in prime factors, we get

46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

∴ \(\sqrt [ 3 ]{ 46656 } =\left( 2\times 2\times 3\times 3 \right) =36\)

**(ix)** Resolving 175616 in prime factors, we get

175616 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7 = (2 x 2 x 2 x 7)

= 56

**(x)** Resolving 91125 in prime factors, we get

91125 = 3 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5

∴ \(\sqrt [ 3 ]{ 91125 } =\left( 3\times 3\times 5 \right) =45\)

**Ex 7.2 Class 8 Maths 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.

**Solution:**

**(i)** False

**(ii)** True

**(iii)** False, as 15^{2} = 225 and 15^{3} = 3375

**(iv)** False, as 8 = 2^{3}, 1728 =12^{3}, etc.

**(v)** False

**(vi)** False, as 10^{3} = 1000, 99^{3} = 970299

**(vii)** True, as 1^{3} = 1, 2^{3} =8.

**Ex 7.2 Class 8 Maths 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.

**Solution:**

**For 1331 :**

Units digit of the cube root of 1331 is 1 as unit’s digit of the cube root of numbers ending in 1 is 1 . After striking three digits from the right of 1331, we get the number 1. Since 1^{3} = 1, so the ten’s digit of the cube root of given number is 1.

∴ \(\sqrt [ 3 ]{ 1331 } =11\)

**For 4913 :**

Units digit of the cube root of 4913 is 7 as unit’s digit of cube root of numbers ending in 3 is 7. After striking three digits from the right of 4913, we get the number 4. As 1^{3} =1 and 2^{3} =8, so 1^{3} < 4 < 2^{3}. Therefore, the ten’s digit of cube root of 4913 is 1.

∴ \(\sqrt [ 3 ]{ 4913 } =17\)

**For 12167 :**

Unit’s digit of the cube root of 12167 is 3 as unit’s digit of cube root of numbers ending in 7 is 3. After striking three digits from the right of 12167, we get the number 12. As 2^{3} =8 and 3^{3} =27, so 2^{3} < 12 < 3^{3}. So, the ten’s digit of the cube root of 12167 is 2.

∴ \(\sqrt [ 3 ]{ 12167 } =23\)

**For 32768 :**

Unit’s digit of the cube root of 32768 is 2 as unit’s digit of cube root of numbers ending in 8 is 2. After striking three digits from the right of 32768, we get the number 32. As 3^{3} =27 and 4^{3} = 64, so 3^{3} < 32< 4^{3}. So, the ten’s digit of the cube root of 32768 is 3.

∴ \(\sqrt [ 3 ]{ 32768 } =32\)

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