**NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Ex 7.1**

**Question 1.**

**Which of the following numbers are not perfect cubes?**

**(i)** 216

**(ii)** 128

**(iii)** 1000

**(iv)** 100

**(v)** 46656

**Solution.**

**(i) 216**

**(ii)** **128**

**(iii) 1000**

**(iv) 100**

**(v) 46656**

**Question 2.**

**Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.**

**(i)** 243

**(ii)** 256

**(iii)** 72

**(iv)** 675

**(v)** 100

**Solution.**

**(i) 243**

**(ii) 256**

**(iii) 72**

**(iv) 675**

**(v) 100**

**Question 3.**

**Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.**

**(i)** 81

**(ii)** 128

**(iii)** 135

**(iv)** 192

**(v)** 704

**Solution.**

**(i) 81**

**(ii) 128**

**(iii) 135**

**(iv) 192**

**(v) 704**

**Question 4.**

Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?

**Solution.**

Volume of a cuboid = 5 x 2 x 5 cm3.

Since there is only one 2 and only two 5’s in the prime factorization, so, we need 2 x 2 x 5, i.e., 20 to make a perfect cube. Therefore, we need 20 such cuboids to make a cube.

**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 ⇒ 152 = 225, 153 = 3375

**(iv)** False ⇒ 123 = 1728

**(v)** False ⇒ 103 = 1000, 993 = 970299

**(vi)** False ⇒ 103 = 1000, 993 = 970299

**(vii)** True ⇒ 13 = 1; 23 = 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, 1331−−−−√3=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, 4913−−−−√3=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, 12167−−−−−√3=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, 32768−−−−−√3=32.