Bunuel
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What is the value of 3(root5(root3(...), where the given expression[#permalink]17 Jun 2020, 05:48
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What is the value of \(3\sqrt{5\sqrt{3\sqrt{5\sqrt{...}}}}\), where the given expression extends to an infinite number of roots?
A. \(3\sqrt{5}\)
B. \(3\sqrt[3]{75}\)
C. 15
D. \(3\sqrt{75}\)
E. 75
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Bunuel
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Joined: 02 Sep 2009
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Re: What is the value of 3(root5(root3(...), where the given expression[#permalink]17 Jun 2020, 05:50
Expert Reply
Bunuel
What is the value of \(3\sqrt{5\sqrt{3\sqrt{5\sqrt{...}}}}\), where the given expression extends to an infinite number of roots?
A. \(3\sqrt{5}\)
B. \(3\sqrt[3]{75}\)
C. 15
D. \(3\sqrt{75}\)
E. 75
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What is the value of 3(root5(root3(...), where the given expression[#permalink]17 Jun 2020, 05:57
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Bunuel
What is the value of \(3\sqrt{5\sqrt{3\sqrt{5\sqrt{...}}}}\), where the given expression extends to an infinite number of roots?
A. \(3\sqrt{5}\)
B. \(3\sqrt[3]{75}\)
C. 15
D. \(3\sqrt{75}\)
E. 75
Are You Up For the Challenge: 700 Level Questions
Let, \(3\sqrt{5\sqrt{3\sqrt{5\sqrt{...}}}} = x\)
i.e. \(3\sqrt{5\sqrt{x}} = x\)
Squaring both sides
i.e. \(9*5\sqrt{x} = x^2\)
Squaring both sides AGAIN
i.e. \(9^2*5^2*x = x^4\)
i.e. \(3^3*3*5^2 = x^3\)
Taking cube root both sides
i.e. \(3\sqrt[3]{75} = x^3\)
Answer: Option B
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yashikaaggarwal
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Re: What is the value of 3(root5(root3(...), where the given expression[#permalink]17 Jun 2020, 06:20
Let 3√5√3√5√3............∞ = Y
3√5√Y = Y
Squaring both sides
9*5√Y = Y^2
Squaring again
81*25*Y = Y^4
3*3*3*3*5*5 = Y^3
Y = 3³√75
Answer is B
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Kinshook
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Re: What is the value of 3(root5(root3(...), where the given expression[#permalink]28 May 2024, 23:28
[quote="Bunuel"]What is the value of \(3\sqrt{5\sqrt{3\sqrt{5\sqrt{...}}}}\), where the given expression extends to an infinite number of roots?
\(x^2 = 9×5\sqrt{x}\)
\(x^4 = 81×25x\)
\(x^3 = 3^3×75\)
\(x = 3\sqrt[3]{75}\)
IMO B
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gmatclubot
Re: What is the value of 3(root5(root3(...), where the given expression[#permalink]
28 May 2024, 23:28