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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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05 Jul 2018, 03:55
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Difficulty:

5% (low)

Question Stats:

89% (00:44) correct 11% (00:55) wrong based on 48 sessions

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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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05 Jul 2018, 04:37
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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05 Jul 2018, 14:12
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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06 Jul 2018, 01:24

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.

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

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09 Jul 2018, 18:56
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

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Re: The operation denoted by the symbol £ is defined for all real numbers &nbs [#permalink] 09 Jul 2018, 18:56
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