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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 8 |

Subject | Maths |

Chapter | Chapter 7 |

Exercise | Class 8 Chapter 7 Cubes and Cube Roots Exercise 7.2 |

Number of Questions Solved | 6 |

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

**NCERT TEXTBOOK EXERCISES**

**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, $\sqrt [ 3 ]{ 32768 } =32$

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

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