+0  
 
+1
423
10
avatar+19 

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

Thanks in advance!

 Jun 13, 2018
edited by TheOutlaw  Jun 14, 2018
 #1
avatar
+1

Since 98 =2 x 7^2, it therefore follows that if we multiply 98 x [2^3 x 7^2] =98 x 392 =

[98 x 392]^1/4 =[ 2^4 x 7^4]^1/4 =2 x 7 = 14.

 Jun 14, 2018
edited by Guest  Jun 14, 2018
 #2
avatar+19 
+1

It says this is incorrect, plus 38416^1/4 is not 14. Does anyone have an answer that they know is right and that they can explain?

TheOutlaw  Jun 14, 2018
 #3
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What do you mean 38,416^(1/4) is NOT 14?. Enter 38,416 in a calculator and take its square root TWICE, you should get 14.

 Jun 14, 2018
 #4
avatar+19 
+1

Sorry, my bad... but it still says 14 is incorrect.

 Jun 14, 2018
 #10
avatar+28468 
+1

It isn't k that is 14.  k is 392.

Alan  Jun 14, 2018
 #7
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-2

U are terrible at math.

 Jun 14, 2018
 #8
avatar+19 
+2

Well then let’s see YOU solve this Mr. Genius, everyone has different experience with math.

TheOutlaw  Jun 14, 2018
 #9
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+1

You can multiply 98 by a fraction such as 8/49 and you get: 98 x 8 / 49 = 16^1/4 =2.

But your question says "positive integer", or "whole number", so I can't see a smaller number than 392.

 Jun 14, 2018

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