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.