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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