What is the simplified form of sqrt r^49?

Question

accidentalaichan · Answer

$$\sqrt{r ^{49}}$$

anonymous · Answer

7

jdoe0001 · Answer

heheh

accidentalaichan · Answer

$$r ^{7}$$?

jdoe0001 · Answer

how many times is "2" into 49?

jdoe0001 · Answer

49 is an odd number, thus it'd end up with some remainder of 1
but the amount of "2" into ... will be?

accidentalaichan · Answer

I know it's 7, but this is why I'm confused.

jdoe0001 · Answer

hmm how do you know is 7 anyway?

accidentalaichan · Answer

There has to be two rational numbers that create the square. Otherwise, it's not a perfect square.

jdoe0001 · Answer

well.... so you're saying that $\bf r^{49} = 7$   whatever happened to the "r"?    it sorta went "missing in action"

jdoe0001 · Answer

ahemm mehh anyhow    $\bf \sqrt{r^{49}} = 7$   rather

accidentalaichan · Answer

It'd have to be $$7r \sqrt{r} $$, because you'd multiply 7r by r and get r^49

accidentalaichan · Answer

At least that's what the lesson says

jdoe0001 · Answer

well.   that'd be true for 49r.... even then.. the "r" is sorta missing

jdoe0001 · Answer

how many times does "2" go into 49 you think?

accidentalaichan · Answer

24.5

jdoe0001 · Answer

24.5   yes.... well. if we throw away the .5  
24 times

so 24 * 2 = 48
so  $\Large \bf  { \sqrt{r^{49}}\to \sqrt{r^{48+1}}\to \sqrt{r^{24\cdot 2+1}}\to 
\sqrt[{\color{red}{ 2}}]{(r^{24})^2\cdot r} }$

accidentalaichan · Answer

So, I'm guessing it is $$r ^{24}\sqrt{r}$$ ?

dan815 · Answer

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