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 ​\( \dfrac{343}{27}~m^2 \)​.

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