SOLUTION: Q. If {{{a = sqrt(3) + sqrt(5)}}} ; b={{{sqrt(sqrt(3)+sqrt(5))}}} and {{{r=a/b}}}, then real no. r satisfies the inequality ______ . Options: a) {{{sqrt(2) < r < 2}}} b) {{{(1/s

Algebra ->  Inequalities -> SOLUTION: Q. If {{{a = sqrt(3) + sqrt(5)}}} ; b={{{sqrt(sqrt(3)+sqrt(5))}}} and {{{r=a/b}}}, then real no. r satisfies the inequality ______ . Options: a) {{{sqrt(2) < r < 2}}} b) {{{(1/s      Log On


   

Question 971212: Q. If a+=+sqrt%283%29+%2B+sqrt%285%29 ; b=sqrt%28sqrt%283%29%2Bsqrt%285%29%29 and r=a%2Fb, then real no. r satisfies the inequality ______ .
Options:
a) sqrt%282%29+%3C+r+%3C+2
b) %281%2Fsqrt%282%29%29+%3C+r+%3C+sqrt%282%29
c) 2+%3C+r+%3C+sqrt%285%29
d)sqrt%285%29+%3C+r+%3C+3
Please give the solution process. The expression is directly given in r. I am unable to write the question in one go, so I used variables 'a' and 'b' for numerator and denominator.
PS: I have tried rationalizing and got upto r%5E2+=+sqrt%283%29+%2B+sqrt%285%29
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
a = square root(3) + square root(5) = 3.968118785
b = square root(a) = 1.992013751
a/b = 3.968118785 / 1.992013751 = 1.992013751
answer is a.
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alternate solution
a = square root(3) + square root(5)
r = a / a^(1/2) = ((a^(1/2)) * (a^(1/2))) / (a^(1/2)) = a^(1/2)
now substitute for a
r = (square root(3) + square root(5))^(1/2) = 1.992013751
answer is a.