# Blackberry publications class 8 maths cube and cube root

### 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 ​$$\dfrac{343}{27}~m^2$$​.