Question

Explain how you would find the exact value of 3 over the square root of 8.

Answer 1

\[\frac{ 3 }{ \sqrt{8} }\]

Answer 2

\[\frac{3}{\sqrt{8}}\]?

Answer 3

if you want to write this is simplest radical form, multiply top and bottom by \(\sqrt{2}\)

Answer 4

you get
\[\frac{3}{\sqrt{8}}\times \frac{\sqrt{2}}{\sqrt{2}}=\frac{3\sqrt{2}}{\sqrt{16}}=\frac{3\sqrt{2}}{4}\]

Answer 5

Where do you get sqrt(2) from?

Answer 6

although... i have to add, there is nothing more EXACT about either form
the second one is written in simplest radical form
the first one is not

Answer 7

i got it because it works
if you multiply \(8\times 2\) you get a perfect square, namely \(16\)

Answer 8

so \(\sqrt{8}\times \sqrt{2}=\sqrt{16}=4\) and you have no radical left in your denominator

Answer 9

ahh okay. Understandable.

Answer 10

now ask your math teacher the following question:
why is \(\frac{3\sqrt{2}}{4}\) more EXACT than \(\frac{3}{\sqrt{8}}\)

i would love to know the answer

Answer 11

Good idea! :p

Answer 12

what the question is really asking is "write \(\frac{3}{\sqrt{8}}\) in simplest radical form" which actually has a definition
one condition is that there should be no radical in the denominator

Answer 13

lol Satellite, "simplify" lol

Answer 14

well "simplest radical form" actually means something

Answer 15

true

Answer 16

not like "simplify"

Answer 17

i will bet $8 that @Mikeyy1992 math teacher is unclear as to what it means

Answer 18

which is why the problem said "exact"

Answer 19

I will inform exactly what she says (: