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What is the smallest positive integer K such that  \(\sqrt[4]{98 \cdot k}\)  is an Integer?

 

This one got me. Would anyone be generous enough to answer this for me?

Logic  Jun 21, 2018
edited by Logic  Jun 25, 2018

Best Answer 

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Since 98 =2 x 7^2, it, therefore, follows that if we multiply 98 x [2^3 x 7^2] =98 x 392 =[2^4 x 7^4]^1/4 = 2 x 7 = 14. So, the number you are looking for is 392, which gives 14 as an integer.

Guest Jun 21, 2018
 #1
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Best Answer

Since 98 =2 x 7^2, it, therefore, follows that if we multiply 98 x [2^3 x 7^2] =98 x 392 =[2^4 x 7^4]^1/4 = 2 x 7 = 14. So, the number you are looking for is 392, which gives 14 as an integer.

Guest Jun 21, 2018

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