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 |
4 |

Category |
NCERT Solutions |

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

**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) 64**

**(ii) 512**

**(iii) 10648**

**(iv) 27000**

**(v) 15625**

**(vi) 13824**

**(vii) 110592**

**(viii) 46656**

**(ix) 175616**

**(x) 91125**

**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 ⇒ \({ 15 }^{ 2 }\) = 225, \({ 15 }^{ 3 }\) = 3375

**(iv)** False ⇒ \({ 12 }^{ 3 }\) = 1728

**(v)** False ⇒ \({ 10 }^{ 3 }\) = 1000, \({ 99 }^{ 3 }\) = 970299

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

**(vii)** True ⇒ \({ 1 }^{ 3 }\) = 1; \({ 2 }^{ 3 }\) = 8

**Question 3.**

You are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.

**Solution.**

By guess,

Cube root of 1331 =11

Similarly,

Cube root of 4913 = 17

Cube root of 12167 = 23

Cube root of 32768 = 32

**EXPLANATIONS**

**(i)**

Cube root of 1331

The given number is 1331.

**Step 1.** Form groups of three starting from the rightmost digit of 1331. __1__ __331__

In this case, one group i.e., 331 has three digits whereas 1 has only 1 digit.

**Step 2.** Take 331.

The digit 1 is at one’s place. We take the one’s place of the required cube root as 1.

**Step 3.** Take the other group, i.e., 1. Cube of 1 is 1.

Take 1 as ten’s place of the cube root of 1331.

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

**(ii)**

Cube root of 4913

The given number is 4913.

**Step 1.** Form groups of three starting from the rightmost digit of 4913.

In this case one group, i.e., 913 has three digits whereas 4 has only one digit.

**Step 2.** Take 913.

The digit 3 is at its one’s place. We take the one’s place of the required cube root as 7.

**Step 3.** Take the other group, i.e., 4. Cube of 1 is 1 and cube of 2 is 8. 4 lies between 1 and 8.

The smaller number among 1 and 2 is 1.

The one’s place of 1 is 1 itself. Take 1 as ten’s place of the cube root of 4913.

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

**(iii)**

Cube root of 12167

The given number is 12167.

**Step 1.** Form groups of three starting from the rightmost digit of 12167.

12 167. In this case, one group, i. e., 167 has three digits whereas 12 has only two digits.

**Step 2.** Take 167.

The digit 7 is at its one’s place. We take the one’s place of the required cube root as 3.

**Step 3.** Take the other group, i.e., 12. Cube of 2 is 8 and cube of 3 is 27. 12 lies between 8 and 27. The smaller among 2 and 3 is 2.

The one’s place of 2 is 2 itself. Take 2 as ten’s place of the cube root of 12167.

Thus, A/12167 = 23.

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

**(iv)**

Cube root of 32768

The given number is 32768.

**Step 1.** Form groups of three starting from the rightmost digit of 32768.

32 768. In this case one group,

i. e., 768 has three digits whereas 32 has only two digits.

**Step 2.** Take 768.

The digit 8 is at its one’s place. We take the one’s place of the required cube root as 2.

**Step 3.** Take the other group, i.e., 32.

Cube of 3 is 27 and cube of 4 is 64.

32 lies between 27 and 64.

The smaller number between 3 and 4 is 3.

The ones place of 3 is 3 itself. Take 3 as ten’s place of the cube root of 32768.

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

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