Algebra Help (Unsolved)

Question

+1

854

10

+19

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

Thanks in advance!

TheOutlaw Jun 13, 2018

edited by TheOutlaw Jun 14, 2018

Guest · Answer 1 · 2018-06-14T12:02:50

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.

Guest · Answer 2 · 2018-06-14T12:27:55

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.

TheOutlaw · Answer 3 · 2018-06-14T12:36:32

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

Guest · Answer 4 · 2018-06-14T12:44:36

-2

U are terrible at math.

Guest Jun 14, 2018

+19

+2

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

TheOutlaw Jun 14, 2018

Guest · Answer 5 · 2018-06-14T12:57:01

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.