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(2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =

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Joined: 02 Sep 2009
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(2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =  [#permalink]

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New post 17 Sep 2018, 23:37
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

93% (00:26) correct 7% (01:07) wrong based on 67 sessions

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Re: (2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =  [#permalink]

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New post 18 Sep 2018, 00:07
Bunuel wrote:
\((\sqrt{2} + 1)(\sqrt{2} - 1)(\sqrt{3} + 1)(\sqrt{3} - 1)=\)


A. 2

B. 3

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

D. 5

E. 6


Using property of \(a^2 - b^2 = (a+b)*(a-b)\)

\((\sqrt{2} + 1)(\sqrt{2} - 1)(\sqrt{3} + 1)(\sqrt{3} - 1)=(2-1)*(3-1) = 2\)

Answer: option A
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(2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =  [#permalink]

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New post 18 Sep 2018, 01:23

Solution


Given:
    • An expression, \((\sqrt{2} + 1) * (\sqrt{2} − 1) * (\sqrt{3} + 1) * (\sqrt{3} − 1)\)

To find:
    • The value of the given expression

Approach and Working:
    • If we observe, the first two terms, are in the form (a + b) * (a - b), where a = \(\sqrt{2}\) and b = 1
      o Thus, \((√2 + 1) * (√2 − 1) = (√2)^2 – 1^2 = 2 - 1 = 1\)
      o Similarly, \((√3 + 1) * (√3 − 1) = (√3)^2 – 1^2 = 3 - 1 = 2\)

Therefore, \((\sqrt{2} + 1) * (\sqrt{2} − 1) * (\sqrt{3} + 1) * (\sqrt{3} − 1) = 1 * 2 = 2\)

Hence, the correct answer is option A.

Answer: A
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Re: (2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =  [#permalink]

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New post 23 Sep 2018, 15:33
Bunuel wrote:
\((\sqrt{2} + 1)(\sqrt{2} - 1)(\sqrt{3} + 1)(\sqrt{3} - 1)=\)


A. 2

B. 3

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

D. 5

E. 6


Using the difference of squares we have:

[(√2)^2 - 1^2][(√3)^2 - 1^2] = (2 - 1) x (3 - 1) = 1 x 2 = 2

Answer: A
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Re: (2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) = &nbs [#permalink] 23 Sep 2018, 15:33
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