Question

\[\frac{ \sqrt{5\sqrt{5}} }{ \sqrt[8]{25} }\]

Answer 1

\[\frac{ \sqrt{5\sqrt{5}} }{ \sqrt[8]{25} }\]

Answer 2

What is 25 in prime factors?

Answer 3

\[\sqrt{5\sqrt{5}}\]

Answer 4

= \[\sqrt{5} \times \sqrt{5} ?\]

Answer 5

nope, you can't do that, the large radical is over the √5 too

Answer 6

but you can have \[\sqrt{5\sqrt 5}=\sqrt5\sqrt{\sqrt5}\]

Answer 7

If you convert those radicals into indices
\[\large \sqrt[q]x^p= x^{p/q}\]

\[\sqrt{\sqrt5}=({5^{1/2}})^{1/2}=5^{\tfrac12\times\tfrac12}\]

Answer 8

So \[\sqrt{5\sqrt{5}} = 5_{4}^{1} ?\]

Answer 9

yes, so what is

\[\sqrt5\sqrt{5\sqrt5}\]

Answer 10

remember that \[\large a^na^m=a^{n+m}\]

Answer 11

\[\sqrt[?]{25} = 5_{8}^{2}\]

Answer 12

?

Answer 13

* \[\sqrt[8]{25}\]

Answer 14

So \[5_{4}^{1} / 5_{8}^{2} = ?\]

Answer 15

wait a minute,

Answer 16

\[\sqrt{5\sqrt 5}=\sqrt5\sqrt{\sqrt5}\]

\[\qquad\qquad\qquad\sqrt{\sqrt{5}} = 5^{1/4}\]

\[\sqrt{5\sqrt 5}=\sqrt5\times 5^{1/4}\\ \qquad\quad=\]

Answer 17

\[\sqrt[8]{25} = 5^{2/8}\] is right by the way.

Answer 18

\[\sqrt{5} \times 5_{4}^{1} = ?\]

Answer 19

yeah so use \[\sqrt 5=\sqrt[2] 5 =5^{1/2}\]

Answer 20

so \[\sqrt{5\sqrt{5}} = 5_{4}^{1} rigth?\]

Answer 21

2/8 *

Answer 22

nope \[\sqrt{5\sqrt{5}} = (5\times(5)^{1/2})^{1/2}=\]

Answer 23

( 5 x \[5_{4}^{1}\] ) =