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# What is the average (arithmetic mean) of (√8 + √2)^2 and (√8 − √2)^2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What is the average (arithmetic mean) of (√8 + √2)^2 and (√8 − √2)^2 ?  [#permalink]

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17 Oct 2018, 01:23
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:01) correct 12% (01:35) wrong based on 42 sessions

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What is the average (arithmetic mean) of (√8 + √2)^2 and (√8 − √2)^2 ?

A. 4
B. 5
C. 8
D. 10
E. 12

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CEO
Joined: 11 Sep 2015
Posts: 3447
Re: What is the average (arithmetic mean) of (√8 + √2)^2 and (√8 − √2)^2 ?  [#permalink]

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17 Oct 2018, 05:42
Top Contributor
Bunuel wrote:
What is the average (arithmetic mean) of (√8 + √2)² and (√8 − √2)² ?

A. 4
B. 5
C. 8
D. 10
E. 12

(√8 + √2)² = (√8 + √2)(√8 + √2)
= 8 + √16 + √16 + 2
= 8 + 4 + 4 + 2
= 18

(√8 - √2)² = (√8 - √2)(√8 - √2)
= 8 - √16 - √16 + 2
= 8 - 4 - 4 + 2
= 2

So, the average = [(√8 + √2)² + (√8 - √2)²]/2
= [18 + 2]/2
= 20/2
= 10

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Re: What is the average (arithmetic mean) of (√8 + √2)^2 and (√8 − √2)^2 ?   [#permalink] 17 Oct 2018, 05:42
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