SOLUTION: Show that (7+(48)^(1/2))^(1/2) + (7-(48)^(1/2))^(1/2) is a rational number

Question 35672: Show that (7+(48)^(1/2))^(1/2) + (7-(48)^(1/2))^(1/2) is a rational number
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
>
> Show that (7+(48)^(1/2))^(1/2) + (7-(48)^(1/2))^(1/2) is a rational number
= SQRT{7+2SQRT(12)}+SQRT{7-2SQRT(12)}
> =SQRT(4)+SQRT(3)+SQRT(4)-SQRT(3)=2+2=4...RATIONAL NUMBER.HOPE YOU KNOW HOW TO FIND THE ABOVE SQ.RT.IF NOT ,I AM GIVING BELOW 1 EXAMPLE
LET SQRT{7+2SQRT(12)}=SQRT(A)+SQRT(B)....SQUARE BOTH SIDES
7+2SQRT(12)=A+B+2SQRT(AB)
HENCE
A+B=7...................I
AB=12............................II
(A-B)^2=(A+B)^2-4AB=7^2-4*12=1
A-B=1 ...............................................III
EQN.I+EQN.III...2A=8...OR.....A=4
HENCE B=7-A=7-4=3........
THUS SQRT{7+2SQRT(12)}=SQRT(4)+SQRT(3)
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