__CUBE AND CUBE ROOTS__

__CUBE AND CUBE ROOTS__

**EXERCISE 8(A)**

**1.Find the cubes of :**

**(a) 2.4**

**(b) 0.2.5**

**(c) 40**

**(d) 51**

**(e) 1.4**

**(f) 0.09**

**(g) \( 3\dfrac{7}{4} \)**

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

**(i) \( 2\dfrac{18}{11} \)**

**(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 the quotient is a perfect cube ?**

**7.Find the smallest number which divides 784 so that the product be a perfect cube.**

**8.Find the smallest number which multiplies 7744 so that the product be a perfect cube.**

**EXERCISE 8 (B)**

**1.Find the cube root of :**

**(a) 2197**

**(b) 74088**

**(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) \( \sqrt[3]{125}\times\sqrt[3]{125\times729} \)**

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

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

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

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

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

**3.Multiply 5049 by the smallest number so that the product is a perfect cube.Find the number , what is the cube root of the product ?**

**4.Divide 823543 by the smallest number so that the quotient is a perfect cube. Write the number and 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? 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 quotient is a perfect cube ? All find the cube root of the quotient.**

**7.Find the side of a cube whose volume is \( \dfrac{343}{27}~m^2 \).**