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The operation denoted by the symbol £ is defined for all real numbers

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The operation denoted by the symbol £ is defined for all real numbers  [#permalink]

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New post 05 Jul 2018, 04:55
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The operation denoted by the symbol £ is defined for all real numbers a and b as \(a£b = a\sqrt{b}\). What is the value of 3£(2£4)?


A. \(\frac{1}{4}\)

B. \(4\)

C. \(6\)

D. \(6\sqrt{2}\)

E. \(12\)

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The operation denoted by the symbol £ is defined for all real numbers  [#permalink]

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New post 05 Jul 2018, 05:37
Bunuel wrote:
The operation denoted by the symbol £ is defined for all real numbers a and b as \(a£b = a\sqrt{b}\). What is the value of 3£(2£4)?


A. \(\frac{1}{4}\)

B. \(4\)

C. \(6\)

D. \(6\sqrt{2}\)

E. \(12\)


We know that \(a£b = a\sqrt{b}\).
We have been asked to find the value of 3£(2£4)

Step 1: Find the value of (2£4) | \(2£4 = 2\sqrt{4} = 4\)
Step 2: Find the value of 3£(4) | \(3£4 = 3\sqrt{4} = 3*2 = 6\)

Therefore, the value of 3£(2£4) is \(6\)(Option C)
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Re: The operation denoted by the symbol £ is defined for all real numbers  [#permalink]

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New post 05 Jul 2018, 15:12
Bunuel wrote:
The operation denoted by the symbol £ is defined for all real numbers a and b as \(a£b = a\sqrt{b}\). What is the value of 3£(2£4)?


A. \(\frac{1}{4}\)

B. \(4\)

C. \(6\)

D. \(6\sqrt{2}\)

E. \(12\)


(2£4)=3£(2*\(\sqrt{4}\))=3£(2*2)=3£4=\(3\sqrt{4}\)=3*2=6

Ans. (C)
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Re: The operation denoted by the symbol £ is defined for all real numbers  [#permalink]

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New post 06 Jul 2018, 02:24

Solution


Given:
    • £ is an operation defined for all real numbers as a£b = \(a√b\)

To find:
    • The value of 3£(2£4)

Approach and Working:
    • 3£(2£4) = 3£(\(2√4\)) = 3£(2 x 2) = 3£4 = \(3√4\) = 6

Hence, the correct answer is option C.

Answer: C
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Re: The operation denoted by the symbol £ is defined for all real numbers  [#permalink]

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New post 09 Jul 2018, 19:56
Bunuel wrote:
The operation denoted by the symbol £ is defined for all real numbers a and b as \(a£b = a\sqrt{b}\). What is the value of 3£(2£4)?


A. \(\frac{1}{4}\)

B. \(4\)

C. \(6\)

D. \(6\sqrt{2}\)

E. \(12\)


We work from the “inside out,” so we will first evaluate 2£4 and use that value to finish the problem.

2£4 = 2√4 = 2 x 2 = 4

3£4 = 3√4 = 3 x 2 = 6

Answer: C
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Re: The operation denoted by the symbol £ is defined for all real numbers &nbs [#permalink] 09 Jul 2018, 19:56
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