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# The expression (root(8 + root(63)) + (root(8 - root(63))^2 =

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Intern
Joined: 16 Nov 2013
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The expression (root(8 + root(63)) + (root(8 - root(63))^2 =  [#permalink]

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Updated on: 21 Nov 2013, 01:21
1
19
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Difficulty:

35% (medium)

Question Stats:

67% (01:31) correct 33% (01:55) wrong based on 388 sessions

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The expression $$(\sqrt{8 +\sqrt{63}} +\sqrt{8 -\sqrt{63}})^2$$ =

A) 20
B) 19
C) 18
D) 17
E) 16

Originally posted by registerincog on 21 Nov 2013, 01:10.
Last edited by Bunuel on 21 Nov 2013, 01:21, edited 2 times in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 62676
Re: The expression (root(8 + root(63)) + (root(8 - root(63))^2 =  [#permalink]

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21 Nov 2013, 01:24
5
8
registerincog wrote:
The expression $$(\sqrt{8 +\sqrt{63}} +\sqrt{8 -\sqrt{63}})^2$$ =

A) 20
B) 19
C) 18
D) 17
E) 16

$$(\sqrt{8 +\sqrt{63}} +\sqrt{8 -\sqrt{63}})^2=(8 +\sqrt{63})+2\sqrt{(8 +\sqrt{63})(8 -\sqrt{63})}+(8 -\sqrt{63})=16+2\sqrt{64-63}=18$$.

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Joined: 16 Jan 2014
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Re: The expression (root(8 + root(63)) + (root(8 - root(63))^2 =  [#permalink]

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22 Dec 2014, 04:06
C) -> 18. Pretty straight forward.
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Re: The expression (root(8 + root(63)) + (root(8 - root(63))^2 =  [#permalink]

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22 Dec 2014, 14:18
Hi registerincog,

Since it's been over a year since you posted, I'm not sure if you're still around to see this, but this question is more about pattern-recognition than anything else.

Bunuel has already shown how the math works, so I won't rehash that here. Instead, I'll offer some perspective.

The GMAT Quant section is going to test you on a lot of standard math rules/ideas/formulas/etc., but will sometimes test you on these rules in ways that you're not used to thinking about. When you find yourself looking at a question that is based on some "crazy-looking" numbers, then chances are really good that the question is built around a pattern of some kind (and it's a pattern that you KNOW in some other simpler format).

Here, if you ignore the numbers and square root signs, you really just have this:

(X+Y)^2

This is one of 3 Classic Quadratics that you MUST have memorized for Test Day.

(X+Y)^2 = X^2 + 2XY + Y^2

Now you can plug back in the relative values for X and Y and simplify. The "math" won't be fun, but its based on standard arithmetic rules (using radicals, multiplication, combining like terms, etc.).

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Re: The expression (root(8 + root(63)) + (root(8 - root(63))^2 =  [#permalink]

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09 Feb 2020, 04:15
registerincog wrote:
The expression $$(\sqrt{8 +\sqrt{63}} +\sqrt{8 -\sqrt{63}})^2$$ =

A) 20
B) 19
C) 18
D) 17
E) 16

Since the given expression is in the form of (x + y)^2, we can use the fact that (x + y)^2 = x^2 + y^2 + 2xy. Thus:

x^2 = [√(8 + √63)]^2 = 8 + √63

y^2 = [√(8 - √63)]^2 = 8 - √63

2xy = 2[√(8 + √63)][√(8 - √63)] = 2√(8^2 - (√63)^2) = 2√(64 - 63) = 2

Thus, the final answer is 8 + √63 + 8 - √63 + 2 = 18.

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Re: The expression (root(8 + root(63)) + (root(8 - root(63))^2 =   [#permalink] 09 Feb 2020, 04:15
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