Question

What is the exact value of √75/21? @jim_thompson5910 Can you help me out again please? lol.

Answer 1

did you mean "exact value"?

Answer 2

Yeah lol sorry, just finished a Geometry exam xD

Answer 3

Can you factor 75 at all (where one factor is a perfect square)?

Answer 4

Well 75 isn't a perfect square.

Answer 5

that's true, but can you factor 75 into something like k*m where either k or m are perfect squares?

Answer 6

23*3

Answer 7

you mean 25*3?

Answer 8

yeah. man I can't type today lol but yes that's what I meant.

Answer 9

so this means...


sqrt(75) = sqrt(25*3)


sqrt(75) = sqrt(25)*sqrt(3)


sqrt(75) = 5*sqrt(3)

Answer 10

So \[\Large \frac{\sqrt{75}}{21} = \frac{5\sqrt{3}}{21}\]

Answer 11

okay, so now what happens with the 21?

Answer 12

wait a second, is the 21 in the square root as well?

Answer 13

yes it is

Answer 14

alright, that completely changes things

Answer 15

thanks

Answer 16

Sorry I should have made that a bit clearer in the beginning.

Answer 17

that's fine

Answer 18

\[\Large \sqrt{\frac{75}{21}}\]


\[\Large \sqrt{\frac{25*3}{7*3}}\]


\[\Large \sqrt{\frac{25}{7}}\]


\[\Large \frac{\sqrt{25}}{\sqrt{7}}\]


\[\Large \frac{5}{\sqrt{7}}\]


\[\Large \frac{5*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\]


\[\Large \frac{5*\sqrt{7}}{\sqrt{7*7}}\]


\[\Large \frac{5*\sqrt{7}}{\sqrt{49}}\]


\[\Large \frac{5\sqrt{7}}{7}\]


So \[\Large \sqrt{\frac{75}{21}} = \frac{5\sqrt{7}}{7}\]

Answer 19

Oh okay. So where did you get the 7 * 3 from?

Answer 20

21 = 7*3

Answer 21

I factored each with a factor of 3 so the 3's will cancel

Answer 22

ahhh okay that makes sense. Thank you again!!