Question

how do you know if a radical is in its simplest form? i mean is there like a condition to be met?

Answer 1

what's a radical?!

Answer 2

those things

Answer 3

ohk

Answer 4

do you know how?

Answer 5

well these kinda things.....i dont think thr wud be a condition...jus trail nd error

Answer 6

A radical is in its simplest form when you can't factorize the inside the radical thing and simplify it

Answer 7

i see...anything else?

Answer 8

it says in this paper that there are three conditions

Answer 9

\( \color{Black}{\Rightarrow \sqrt{10} = \sqrt{2 \times 5} = \sqrt{10} }\)
You just can't simplify it more

Answer 10

Are you trying to test us?lol

Answer 11

uhmm no

Answer 12

A fraction with radicals is simplified when the denominator is rationalized

Answer 13

i think the last one had something to do with indeces but i cant remember it :/

Answer 14

Lol I dunno about that but my logic applies to all

Answer 15

or was it when there isnt a radical within the radical

Answer 16

Can you give an example?

Answer 17

well for example simplify \[\sqrt{10x^3y^5} \times \sqrt[3]{4x^2y}\]

Answer 18

factor and simplify

Answer 19

In the first one you can cancel out x and y.....

Answer 20

well hmm i see that...what next? after putting out the root i meea

Answer 21

mean*

Answer 22

What did you get in the roots?

Answer 23

\[\large xy \sqrt{10xy} \times \sqrt[3]{4x^2y}\] is that right?

Answer 24

oops y should be squared in the xy part i think

Answer 25

Lol yes

Answer 26

then what?

Answer 27

\( \color{Black}{\Rightarrow xy^2 \times \sqrt{10} \times \sqrt{x} \times \sqrt{y }......etc }\)

Answer 28

i dont get what you're pointing out

Answer 29

Do you know how to get these questions? for example:

\( \color{Black}{\Rightarrow \sqrt{x} \times \sqrt[3]{x} }\)

Answer 30

uhmm...x^1/6?

Answer 31

My personal preference is to use exponents.

\( \color{Black}{\Rightarrow x^{1 \over 2} \times x^{1 \over 3} }\)

You add the exponents when base is same and you are multiplying

Answer 32

oh oh yeah add exponENTS *facepalm* well what about in 10 and 4? it's not same base anymore

Answer 33

\( \color{Black}{\Rightarrow \sqrt{10} \times \sqrt[3]{4} }\)
Some thing like this?

Answer 34

then? how do you express it as one index??

Answer 35

Lol here you are a free bird.....use the internet to figure out

Answer 36

Oh I see how to do this yes

Answer 37

i come here to learn and you're directing me to the net?!

Answer 38

\( \color{Black}{\Rightarrow \sqrt{10} = \sqrt{2} \times \sqrt{5} }\)

Answer 39

i thought the purpose of this site was to teach people???

Answer 40

i see no logic in telling people to go away and learn from the net...the purpose i came here instead of the net is because i didnt find my answer in the net right?!

Answer 41

Hmm but I just told you

Answer 42

i still dont see your point btw

Answer 43

Do you know that:;

\( \color{Black}{\Rightarrow \sqrt{a} \times \sqrt{b} = \sqrt{ab} }\)?

Answer 44

yeah but how does iot apply to 10 and 4

Answer 45

Now look:

\( \color{Black}{\Rightarrow \sqrt{10} = \sqrt{2} \times \sqrt{5} }\)
agree?

Answer 46

yeah

Answer 47

Aww snap!

Answer 48

\( \color{Black}{\Rightarrow \sqrt[3]{4} = \sqrt[3]{2} \times \sqrt[3]{2} }\)
Agree again?

Answer 49

yes

Answer 50

\( \color{Black}{\Rightarrow \sqrt{2} \times \sqrt{5} \times\sqrt[3]{2} \times \sqrt[3]{2} }\)
Convert into exponents and see :D

Answer 51

what??

Answer 52

\( \color{Black}{\Rightarrow 2^{1 \over 2} \times 5^{1 \over 2} \times 2^{1 \over 3} \times 2^{1 \over 3} }\)

Answer 53

Add the exponents of 2.

Answer 54

10^1/2 you just went back to the old one lol..long cut

Answer 55

So do you understand how to do it?

Answer 56

nope..what's after 10^1/2

Answer 57

Lol I told you that:

\( \color{Black}{\Rightarrow \sqrt{10} = \sqrt{2} \times \sqrt{5} = 2^{1 \over 2} \times 5^{1 \over 2} }\)

Answer 58

you're circling me around you know

Answer 59

uh-oh....you're getting circled. Twid me

Answer 60

okay...