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(8 sqrt2-4)^2

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(8 sqrt2-4)^2 [#permalink] New post 12 Feb 2020, 10:26
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Question Stats:

81% (00:58) correct 18% (01:26) wrong based on 27 sessions
\(\left( \begin{array}{cc} \frac{8 \sqrt{2} - 4}{4} \end{array} \right) ^2 = \)


A. \(9-4 \sqrt{2}\)

B. \(36-16 \sqrt{2}\)

C. \(8\)

D. \(9\)

E. \(32 \sqrt{2}\)


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[Reveal] Spoiler: OA

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Re: (8 sqrt2-4)^2 [#permalink] New post 12 Feb 2020, 10:37
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Carcass wrote:
\(\left( \begin{array}{cc} \frac{8 \sqrt{2} - 4}{4} \end{array} \right) ^2 = \)


A. \(9-4 \sqrt{2}\)

B. \(36-16 \sqrt{2}\)

C. \(8\)

D. \(9\)

E. \(32 \sqrt{2}\)


Kudos for the right answer and explanation


One approach to quickly arrive at the answer is to estimate the value of the given expression.

By test day, all students should have the following approximations memorized:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, our approximation will go as follows: \((\frac{8 \sqrt{2} - 4}{4})^2 ≈ (\frac{8(1.4)- 4}{4}) ^2\)

\(≈ (\frac{11- 4}{4}) ^2\)

\(≈ (\frac{7}{4}) ^2\)

\(≈ (\frac{49}{16})\)

\(≈ 3 \)


Now let's estimate each answer choice....

A. \(9-4 \sqrt{2}≈9-4(1.4)≈9-6≈3\) Nice!! KEEP

B. \(36-16 \sqrt{2}≈36-16(1.4)≈36-23≈13\) Not close. ELIMINATE

C. \(8\) Not close. ELIMINATE

D. \(9\) Not close. ELIMINATE

E. \(32 \sqrt{2}≈32(1.4)\) Not close. ELIMINATE
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Re: (8 sqrt2-4)^2 [#permalink] New post 12 Feb 2020, 10:58
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I think here the best approach is algebraical, if you do know what to do, you can solve it in 20 seconds


Inside the parentheses will become

\(\frac{8 \sqrt{2}}{4} -\frac{4}{4}\) raised to the power of two

Simplify

\((2 \sqrt{2} - 1 )^2\)

\(4 (\sqrt{2})^2+1-4 \sqrt{2}\)

\(8+1 -4 \sqrt{2}\)

A is the answer
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Re: (8 sqrt2-4)^2 [#permalink] New post 13 Feb 2020, 23:03
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Carcass wrote:
\(\left( \begin{array}{cc} \frac{8 \sqrt{2} - 4}{4} \end{array} \right) ^2 = \)


A. \(9-4 \sqrt{2}\)

B. \(36-16 \sqrt{2}\)

C. \(8\)

D. \(9\)

E. \(32 \sqrt{2}\)


Kudos for the right answer and explanation




I would go with simplifying by rewriting every number as 2 to some power:

\(((2 ^3 * 2 ^\frac{1}{2} - 2 ^2 )*2 ^(-2) ) ^2 \)

That simplifies to:

\((2 ^\frac{3}{2} - 1 ) ^2 \)

That simplifies to:

\(2 ^3 - 2*2 ^\frac{3}{2} + 1 \) = \(9-4 \sqrt{2}\)

Answer A
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Re: (8 sqrt2-4)^2 [#permalink] New post 27 Apr 2020, 03:33
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My approach:


((8√2-4)*(8√2-4))/16

(128-64√2+16)/16

(16*(8-4√2+1))/16

8-4√2+1

9-4√1
Re: (8 sqrt2-4)^2   [#permalink] 27 Apr 2020, 03:33
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