sqrt (7* sqrt(7* sqrt (7*...)))=(343)^(y-1) then y is euqal to

a) 2/3 b) 1 c) 4/3 d) 3/4

• let sqrt (7* sqrt(7* sqrt (7*...)))=x
  =>x=sqrt(7*x)
  =>x^2=7x
  =>x^2-7x=0
  =>x=0,7
  neglect 0, x=7
  now 7 = (343)^(y-1)
  => (7^3)^(1/3)= (343)^(y-1)
  => (343)^(1/3)= (343)^(y-1)
  => (1/3)=(y-1)
  => 3y-3=1
  => 3y=4
  => y=4/3 ans
• 12 years agoHelpfull: Yes(7) No(0)
• Trick:-- sqrt (p* sqrt(p* sqrt (p*...)))= p
  P=7
  then, sqrt (7* sqrt(7* sqrt (7*...))= (343)^(y-1)
  ====> 7 = (343)^(y-1)
  ====> 7 = 7^3(y-1)
  ====> 1=3(y-1)
  ====> y=4/3
• 12 years agoHelpfull: Yes(4) No(0)
• Sqrt(a*sqrt(a*(sqrt(a*..........)))=a [ According to the Rules of Surds]
  Therefore,
  sqrt(7 *(sqrt 7 *(sqrt 7 *.......)))= 7
  =>7=(343)^(y-1)
  =>7^1=(7^3)^(y-1)
  =>1=3y-3 [since base is equal in both sides]
  =>y=4/3.
• 7 years agoHelpfull: Yes(0) No(0)