Question

What is the simplest form of the radical expression?

Answer 1

\[\frac{ \sqrt{2}+\sqrt{5} }{ \sqrt{2}-\sqrt{5} }\]

Answer 2

well you cant really have a whole number for the square root of these two numbers. the best thing we could do is round the decimal. so the square root of 2 is about 1.41 and the square root of 5 is about 2.24. if we had those two together on the top, we would get 3.65.

Answer 3

then if we subtract those two, we would get -0.83.

Answer 4

now did you want the two answers divided or into a fraction?

Answer 5

it says i need to get them in simplest form and show work but it can't be rounded. it must be exact

Answer 6

oh. maybe we would round the decimal to a whole number then

Answer 7

I'm pretty sure they want you to multiply by the conjugate. Give me a minute to work it out then I'll explain.

Answer 8

that makes no sense :( i am not supposed to round this ever

Answer 9

ok

Answer 10

i know the answer will likely still have square roots but be simpler?

Answer 11

maybe you just need someone else

Answer 12

jam is replying. he helped me really well. let him take over

Answer 13

sorry for not helping. :/

Answer 14

When you are dealing with radicals, they don't like to see them in the denominator.

Conjugate example. 1 + sqrt2 has a conjugate of 1 - sqrt2

So for this question, multiply top and bottom by sqrt2 + sqrt5. That's what I think they want you to do.

Answer 15

(sqrt2 + sqrt5) / (sqrt2 - sqrt5) times (sqrt2 + sqrt5) / (sqrt2 + sqrt5)
= (2 + 2(sqrt5)(sqrt2) + 5) / 2 - 5
= [7 + 2(sqrt5)(sqrt2)] / (-3)
= [-7 - 2(sqrt5)(sqrt2)]/3
That's what I think the answer is.

Answer 16

\[-\frac{( \sqrt{2}+\sqrt{5} )^2}{ 3 }\] is how it comes up for me, is this right?

Answer 17

my answer makes no sense at all

Answer 18

That's exactly what I got. I just multiplied out the top.

Answer 19

what?

Answer 20

where did the 7+2 part come from?

Answer 21

or -7-2

Answer 22

sqrt2 times sqrt2 = 2
sqrt5 times sqrt5 = 5

Answer 23

simpler example:
I'll draw:

Answer 24

Do you see how to expand these sort of expressions?

Answer 25

\[(3+\sqrt{2})\times(3+\sqrt{2})=93+\sqrt{2}+3\sqrt{2}+4=9+6\sqrt{2}+4=13+3\sqrt{2}\]
is this what you wrote?

Answer 26

\[(3+\sqrt{2})\times(3+\sqrt{2})=93+\sqrt{2}+3\sqrt{2}+4=9+6\sqrt{2}+4=13+6\sqrt{2}\]
so this then?

Answer 27

its hard to read, so just tell me if this is what you meant to write

Answer 28

Let me start over. There were a couple of mistakes in mine.

Answer 29

use the equation button pls

Answer 30

Thanks for telling me about the equation button. I didn't know about it.
Do you see how to expand the brackets now? root 2 times root 2 equals 2.

Answer 31

\[(3 + \sqrt{2}) \times (3 + \sqrt{2}) = 9 + 3\sqrt{2} + 3\sqrt{2} + 2\]

Answer 32

\[9 + 2 + 3\sqrt{2} + 3\sqrt{2} = 11 + 6\sqrt{2}\]

Answer 33

That's how I expanded the original question.

Answer 34

Now I'll type in the end of your solution.

Answer 35

\[(\sqrt{2} + \sqrt{5}) \times (\sqrt{2} + \sqrt{5}) = 2 + \sqrt{2}\sqrt{5}+\sqrt{2}\sqrt{5} + 5\]

Answer 36

So that's what is on top and there's a -3 in the denominator. I gathered like terms and moved the minus sign up to the numerator to get:

Answer 37

\[(-7 - 2\sqrt{5}\sqrt{2})\div3\]

Answer 38

OS keeps freezing up on me for some reason, I think I can piece together an answer from the information given. Thanks for bearing with me.

Answer 39

No problem. Your answer was right. I think they would want you to expand the numerator instead of leaving it squared. So that's what I did.

Answer 40

Do you want me to attach a file with the whole thing written out? It might be clearer that way?

Answer 41

I can't attach it right now. Problems with my scanner. I'll try again later.

Answer 42

alright, thanks @jam333

Answer 43

My answer could be wrong, but I think that's what they want.
What level of school are you in? It helps so I know what to send you. I can send reviews of important concepts.