What is the value of 3(root5(root3(...), where the given expression (2025)

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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(root5(root3(...), where the given expression (15)

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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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What is the value of 3(root5(root3(...), where the given expression (21)

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Bunuel

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Re: What is the value of 3(root5(root3(...), where the given expression[#permalink]17 Jun 2020, 05:50

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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

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What is the value of 3(root5(root3(...), where the given expression (25)

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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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What is the value of 3(root5(root3(...), where the given expression (29)

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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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What is the value of 3(root5(root3(...), where the given expression (31)

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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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What is the value of 3(root5(root3(...), where the given expression (36)

gmatclubot

Re: What is the value of 3(root5(root3(...), where the given expression[#permalink]

28 May 2024, 23:28

What is the value of 3(root5(root3(...), where the given expression (2025)
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