__CUBE AND CUBE ROOTS__

__EXERCISE 4 (A)__

### 1.Write (T) for True or (F) for false:

**(i) The cube root of 8000 is 200.**

**(ii) Each prime factor appears 3 times in its cube.**

**(iii) \( \sqrt[3]{27+64}=\sqrt[3]{27}+\sqrt[3]{64} \)**

**(iv) For an integer a, \( a^3 \) is always greater than \( a^2 \).**

**(v) The least number by which 72 must be divided to make it a perfect cube is 9.**

### 2.Find the cubes of the following numbers.

**(i) 8**

**(ii) \( -15 \)**

**(iii) 600**

### 3.

**(i) \( \dfrac{5}{6} \)**

**(ii) \( \dfrac{-7}{9} \) **

**(iii) \( 1\dfrac{3}{5} \)**

### 4.

**(i) 0.03**

**(ii) 1.7**

**(iii) \( -0.008 \)**

### 5.Which of the following numbers are perfect cubes?

**65, 128, 243, 512, 900, 1728, 4096**

### 6.Find the cube root of the following numbers by prime factorization method.

**(i) 5832**

**(ii) 91125**

**(iii) \( -9261 \)**

**(iv) \( \dfrac{125}{343} \)**

**(v) \( -\dfrac{2744}{4096} \)**

**(vi) \( -5\dfrac{104}{125} \)**

### 7.Evaluate:

**(i) \( \sqrt[3]{1.331} \)**

**(ii) \( \sqrt[3]{0.003375} \)**

### 8.What is the smallest number by which each of the following numbers must be multiplied so that the product is a perfect cube.Also, find cube root of the product.

**(i) 1125**

**(ii) 6912**

**(iii) 47916**

### 9.Find the smallest number by which each of the following numbers must be divided so that quotient is a perfect cube. Also, find the cube root of the product.

**(i) 3584**

**(ii) 1458**

**(iii) 120393**

### 10.Find the value of :

**(i) \( \sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064} \)**

**(ii) \( \bigg\{(5^2+\sqrt{10^2})\bigg\}^3 \)**

**(iii) \( \sqrt[3]{686}\times\sqrt[3]{500} \)**