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Exponents/Radicals: Simplify ( 1 / 3 - sqrt8 ) ²

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

Exponents/Radicals: Simplify ( 1 / 3 - sqrt8 ) ²

by II » Sat Dec 29, 2007 4:49 pm

Simplify:

( 1 / 3-√8 ) ²

A) 9+√8
B) 9+2√8
C) 9+6√8
D) 17+2√8
E) 17+6√8

Can you please let me know how you get to the answer.
Thanks.
II

Last edited by II on Tue Apr 29, 2008 6:34 am, edited 2 times in total.

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Source: Beat The GMAT — Problem Solving | Sat Dec 29, 2007 4:49 pm

beingAndNothing: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Fri Sep 14, 2007 10:35 am; Thanked: 1 times

by beingAndNothing » Sat Dec 29, 2007 8:14 pm

1/(3-sqrt(8)) = 3+sqrt(8)/(9 - 8) = 3+sqrt(8)

3+sqrt(8) = 9 + 8 + 6sqrt(8) = 17 + 6 sqrt(8)

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Sun Dec 30, 2007 1:19 am

beingAndNothing wrote:1/(3-sqrt(8)) = 3+sqrt(8)/(9 - 8) = 3+sqrt(8)

3+sqrt(8) = 9 + 8 + 6sqrt(8) = 17 + 6 sqrt(8)

can you please explain in more detail ? thanks.

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starxx68: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Dec 17, 2007 9:24 pm; Thanked: 1 times

by starxx68 » Sun Dec 30, 2007 8:05 am

Basically, you square the denominator (3-sqrt(8)) using FOIL, getting 17-6sqrt(8).

Then, you rationalize the denominator by multiplying the whole fraction (1/(3-sqrt(8)) by (17+6sqrt(8))/(17+6sqrt(8)). You find that the denominator gives you 289-288 = 1, so you end up just with (17+6sqrt(8)) in the numerator.

The smiley faces = the number 8. I'm not sure why they become smileys.