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Solution
The correct option is C
5
For a number to be a perfect
cube, its prime factors should be expressed as triplets.
By prime factorization, we get
1715=7×7×7×5
We have three 7’s but only one 5 so we need to divide the number by 5.
∴ We need to divide it by 5, then it becomes cube of 7 i.e 343
Question Papers
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What is the smallest number by which 6912 must be divided so that the quotient obtained will have a perfect cube root?
Given: A number 6912 . To do: To find the smallest number by which 6912 must be divided so that the number formed is a perfect cube. Therefore, we should divide 6912 by 22=4 2 2 = 4 , the smallest number to get 1728 which is a cube of 12 .
Which smallest natural number should 53240 be divided so that the quotient is a perfect cube?
Hence the smallest number by which 53240 should be divided to make it a perfect cube is 5. The perfect cube in that case is = 10648.
What is the smallest number by which 88209 should be divided to make the quotient a perfect cube?
Hence, the correct answer is 121.
What is the smallest number by which 704 must be divided so that quotient is a perfect square?
Here, the prime factor 11 is not grouped as a triplet. Hence, we divide 704 by 11, so that the obtained number becomes a perfect cube. Hence the smallest number by which 704 should be divided to make a perfect cube is 11.