Question

Use a calculator to find the value of the expression. Then show that the calculated value is correct.

frac{sqrt{2}+sqrt{6}}{sqrt{2+sqrt{3}}} =2

~~I have tried subbing in a common variable to prove this, such as m= sqrt{2} and using that, put it into the equation so that the equation now reads:
frac{m+(m^2+4)^{1/2}}{sqrt{2+(m^2+1)^{1/2}}}

I have not gotten very far with that though, I may be doing it completely wrong.So any insight/help is appreciated! Thanks!

Answer 1

\[\frac{\sqrt{2}+\sqrt{6}}{\sqrt{2+\sqrt{3}}} =2 \] is the original equation.

Answer 2

The equation I have come up with (when I sub in m as equaling\[\sqrt{2}\] is:
\[\frac{m+(m^2+4)^{1/2}}{\sqrt{2+(m^2+1)^{1/2}}} \]

Answer 3

the values comes around 4.8 use your calculator again

Answer 4

...Oh wait you mean the calculated answer of the original equation isn't 2?..let me check..

Answer 5

hmm... for this equation
\[\frac{\sqrt{2}+\sqrt{6}}{\sqrt{2+\sqrt{3}}} \]
is still got it equaling 2..

Answer 6

oh sorry i got denominator (2)^1/2 + 3^1/2 ....i'm on your question thanks :)

Answer 7

Oh not a problem! :)

Answer 8

Hey I got it !!!

Answer 9

No way!! I spent like 2 hours on this today!

Answer 10

2^1/2 +6^1/2
y = -------------
( 2 + 3^1/2)^1/2

now just square both sides

Answer 11

2 + 6 + 2. (12)^1/2
y^2 = -----------------
2 + 3^1/2



8 + 2 . 12^1/2
y^2 = -------------
2 + 3^1/2

Answer 12

2( 4 + (4.3)^1/2)
y ^2 = ------------
2 + 3^1/2

Answer 13

2 * 4^1/2 ( 4^1/2 + 3^1/2)
y^2 = ----------------------------
2 + 3^1/2



y^2 = 4.( 2 + 3^1/2)
--------------
2 + 3^1/2


y^2 = 4


y = 2

Answer 14

I squared just because it helps get rid of that whole under root .... and it makes easy to think ...

Answer 15

Okay! I getcha~ my only question is after you square both sides where do you get the 2. (12)^1/2 from?

Answer 16

(12)^1/2 = (4.3)^1/2 = (4)^1/2 . (3)^1/2 = 2 . (30^1/2

Answer 17

Oh okay! Well thank you so much Ishaan!! That makes sense! ( I think I was just overthinking the whole thing! ) :)

Answer 18

: )