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.