Question

10. Find the smallest number by which the following numbers must be multiplied so that the productsare perfect cubes.
(a) 5,324 (b) 1,323 ( 27,783 (d) 12,348 ( e) 3,125 (f) 1,01,306​

Answer 1

Answer:

e

Step-by-step explanation:

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Answer 2

a. 2

b. 7

c. 9

d. 6

e. 5

f. 4

Step-by-step explanation:

a. 5324= 2×2×11×11×11

= 2²×11³

Thus, 5324 should be multiplied by 2 to get a perfect cube

b. 1323= 3×3×3×7×7

= 3³×7²

Thus, 1323 should be multiplied by 7 to get a perfect cube

c. 27783= 3×3×3×3×7×7×7

= 3⁴×7³

Thus, 27783 should be multiplied by 9(3²) to get a perfect cube

d. 12348= 2×2×3×3×7×7×7

= 2²×3²×7³

Thus, 12348 should be multiplied by 6(2×3) to get a perfect cube

e. 3125= 5×5×5×5×5

= 5⁵

Thus, 3125 should be multiplied by 5 to get a perfect cube

f. 101306= 2×37×37×37

= 2¹×37³

Thus, 101306 should be multiplied by 4(2²) to get a perfect cube