__CUBE AND CUBE ROOTS__

__EXERCISE (A)__

### 1.Find the cube of :

**(a) 2.4**

**(b) 0.25**

**(c) 40**

**(d) 51**

**(e) 1.4**

**(f) 0.09**

**(g) \( 3\dfrac{4}{5} \)**

**(h) \( \dfrac{6}{7} \)**

**(i) \( 2\dfrac{8}{11} \)**

**(j) \( 1\dfrac{6}{17} \)**

### 2.Which of the following are perfect cubes ?

**(a) 200**

**(b) 9261**

**(c) 64**

**(d) 4095**

**(e) 864**

### 3.Which of the following numbers are cubes of even natural numbers ?

**(a) 64**

**(b) 216**

**(c) 343**

**(d) 76005**

**(e) 8009**

### 4.Which of the following numbers are cubes of odd natural numbers ?

**(a) 11664 **

**(b) 1331**

**(c) 6859**

**(d) 8640**

**(e) 729**

### 5.What is the smallest number by which 1024 must be divided so that the quotient is a perfect cube ?

### 6.What is the smallest number by which 8640 must be divided so that quotient is a perfect cube ?

### 7.Find the smallest number which divides 784 so that the quotient be a perfect cube.

### 8.Find the smallest number which when multiplied with 7744 gives a perfect cube as the product.

__EXERCISE (B)__

### 1.Find the cube root of :

**(a) 2197**

**(b) 15625**

**(c) 125\( \times \)1331**

**(d) 27 \( \times \)(2744)**

**(e) 91.125**

**(f) -39304**

**(g****) \( 4\dfrac{17}{27} \)**

**(h) -0.000001331**

### 2.Show that :

**(a) **\( \sqrt[3]{512}\times\sqrt[3]{512\times1728}=\sqrt[3]{768} \)

**(b) **\( \sqrt[3]{64}+\sqrt[3]{729}=\sqrt[3]{(64+729)} \)

**(c) **\( \sqrt[3]{216}\times\sqrt[3]{(-8)}=\sqrt[3]{216\times(-8)} \)

**(d) **\( \sqrt{\sqrt[3]{27}+\sqrt[3]{125}}=\sqrt[3]{3+\sqrt[3]{125}} \)****

**(e) **\( \sqrt[3]{\dfrac{-35937}{6859}}=\dfrac{\sqrt[3]{-35937}}{\sqrt[3]{6859}} \)

**(f) **\( \dfrac{\sqrt[3]{9261}}{\sqrt[3]{1000}}=\sqrt[3]{\dfrac{9261}{1000}} \)** **

### 3.Multiply 59049 by the smallest number such that the product is a perfect cube .Find the number, also find the cube root of the product ?

### 4.Divide 823543 by the smallest number so that the quotient is a perfect cube.Find the number and also find the cube root of the quotient ?

### 5.What is the smallest number by which 675 should be multiplied so that the product is a perfect cube? Also,find the cube root of the perfect cube so obtained.

### 6.What is the smallest number by which 2916 should be multiplied so that the product is a perfect cube? Also,find the cube root of the product.