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

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Bunuel
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The operation denoted by the symbol £ is defined for all real numbers [#permalink] 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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C
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The operation denoted by the symbol £ is defined for all real numbers [#permalink] New post   05 Jul 2018, 05:37
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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] 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. \(12\)


3£(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] New post   06 Jul 2018, 02:24
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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] New post   09 Jul 2018, 19:56
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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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The operation denoted by the symbol £ is defined for all real numbers [#permalink] New post   07 Aug 2022, 23:38
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Given that a £ b = \(a\sqrt{b}\) and we need to find the value of 3 £(2£4)

Lets start by finding the value of 2£4

To find 2£4 we need to compare what is before and after £ in 2£4 and a£b

=> We need to substitute a with 2 and b with 4 in a £ b to get the value of 2£4

=> 2 £ 4 = \(2\sqrt{4}\) = 2*2 = 4

=> 3 £(2£4) = 3£4

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

So, Answer will be C
Hope it helps!

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The operation denoted by the symbol £ is defined for all real numbers [#permalink]
07 Aug 2022, 23:38
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