CBSE Class 8 Mathematics Exponents And Powers Worksheet Set 05

EXPONENTS & RADICAL, SQUARES & SQUARE ROOTS, CUBES & CUBE ROOTS

Question. 1. A gardner plants 17956 trees in such a way that there are as many rows as there are trees in each row. The number of trees in a row are :
(a) 136
(b) 164
(c) 134
(d) 166
Answer: C

Question. 2. \(\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}\) is equal to
(a) 0
(b) 2
(c) 1
(d) \(2^{\frac{31}{32}}\)
Answer: D

Question. 3. 'The greatest six digit number which is perfect square is :
(a) 998004
(b) 998006
(c) 998049
(d) 998001
Answer: D

Question. 4. Divide the number 26244 by the smallest number so that the quotient is a perfect cube, so the smallest number is :
(a) 4
(b) 6
(c) 36
(d) 16
Answer: C

Question. 5. The perfect cube nearest to 2750 is :
(a) 2749
(b) 2747
(c) 2744
(d) 2754
Answer: C

Question. 6. The least number which must be added to 4931 to make it perfect square is :
(a) 110
(b) 120
(c) 130
(d) None
Answer: A

Question. 7. The least number which must be subtracted from 18265 to make it a perfect square is:
(a) 20
(b) 30
(c) 40
(d) 50
Answer: C

Question. 8. Least perfect square of 6 digits is :
(a) 998000
(b) 998001
(c) 998002
(d) None of these
Answer: B

Question. 9. A \(8 \times 6 \times 4 \text{ cm}^3\) metallic cube is melted. Find the minimum volume of molten metal which should be added to mould it into a cube whose edge is an x, where x is an integer.
(a) 20
(b) 21
(c) 23
(d) 24
Answer: D

Question. 10. Value of \(\sqrt[3]{392} \times \sqrt[3]{448}\) is
(a) 50
(b) 52
(c) 54
(d) 56
Answer: D

Question. 11. The smallest number by which 137592 should be multiply to make it perfect cube.
(a) 1183
(b) 1180
(c) 1181
(d) None of these
Answer: A

Question. 12. The volumes of two cubes are in the ratio of \(343 : 1331\), the ratio of their edges is .
(a) 7: 10
(b) 7:11
(c) 7: 12
(d) None of these
Answer: B

Question. 13. (5, 12, 15) and (7, 5, 12)
(a) Both are Pythagorean triplets
(b) None of the both is Pythagorean triplet
(c) First is Pythagorean triplet while second is not
(d) Second is Pythagorean triplet while first is not
Answer: B

Question. 14. \(\frac{(65 - 56)^2}{3^2} = ?\)
(a) 8
(b) 9
(c) \(\frac{1}{9}\)
(d) None of these
Answer: B

Question. 15. \((16)^2 \times (4)^2 = ?\)
(a) 4096
(b) 16360
(c) 25360
(d) None of these
Answer: A

Question. 16. \(\left( \frac{15}{8} \times 16 \right)^2 = ?\)
(a) 916
(b) 900
(c) 926
(d) 1966
Answer: B

Question. 17. \(\frac{(16)^2 + (12)^2}{(20)^2} = ?\)
(a) 4
(b) 2
(c) 1
(d) 5
Answer: C

Question. 18. \(\frac{(48 - 8)^2}{40} = ?\)
(a) 40
(b) 80
(c) 15
(d) 150
Answer: A

Question. 19. \((65)^2 - (64)^2 + (1)^2 =?\)
(a) 130
(b) 129
(c) 138
(d) 120
Answer: A

Question. 20. \((57)^2 - (52)^2 = 5 \times ?\)
(a) 109
(b) 108
(c) 5
(d) None of these
Answer: A

Question. 21. If \((65)^2 - (60)^2 = [(55)^2 - (50)^2] \times y\), then the value of y is-
(a) \(\frac{23}{21}\)
(b) \(\frac{28}{21}\)
(c) \(\frac{25}{21}\)
(d) None of these
Answer: C

Question. 22. \(\frac{55 \times 55 - 2 \times 25 \times 55 + 25 \times 25}{30^2} = ?\)
(a) 6
(b) 4
(c) 5
(d) None of these
Answer: D

Question. 23. \(\frac{65 \times 65 + 2 \times 65 \times 35 + 35 \times 35}{65 + 35} = ?\)
(a) 1000
(b) 10
(c) 100
(d) None of these
Answer: C

Question. 24. By studying the numbers given below, find out the missing numbers.
\((1)^2 + (2)^2 + (2)^2 = (3)^2\)
(i) \((4)^2 + (5)^2 + \square^2 = (21)^2\)
(a) 20
(b) 6
(c) 7
(d) 24
(ii) \((5)^2 + \square^2 + (30)^2 = (31)^2\)
(a) 9
(b) 8
(c) 7
(d) 6
Answer: (i) a; (ii) d

Question. 25. The value of \(\sqrt{225}\) is-
(a) 25
(b) 15
(c) 35
(d) 05
Answer: B