exponent and radical simplification

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Lakers09: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Nov 02, 2008 5:49 pm

by Lakers09 » Mon Nov 03, 2008 7:29 pm

Hi All,
I am having trouble attacking this problem. For starters, how do I know that it is a 45-45-90 triagle by the information given? in the first part of the explanation how do they arrive at xrad3

Any help would be great.

Thanks

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Source: Beat The GMAT — Problem Solving | Mon Nov 03, 2008 7:29 pm

stubbornp: Master | Next Rank: 500 Posts; Posts: 496; Joined: Sun May 04, 2008 11:01 pm; Location: mumbai; Thanked: 7 times; GMAT Score:640

by stubbornp » Mon Nov 03, 2008 10:24 pm

let the side of cube be x...ac=x

distance of bc=(3^0.5)x=1.732x

distance of ab=(2^0.5)x=1.414x

difference=1.732x-1.414x=0.318x~==0.3x

0.3x is 30% of x.....hope it clears

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Lakers09: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Nov 02, 2008 5:49 pm

by Lakers09 » Mon Nov 03, 2008 10:42 pm

Thanks so much for your response

how did you arrive at bc=(3^0.5)x and ab=(2^0.5)x ???

distance of bc=(3^0.5)x=1.732x

distance of ab=(2^0.5)x=1.414x

Thanks

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raunekk: Legendary Member; Posts: 1159; Joined: Wed Apr 16, 2008 10:35 pm; Thanked: 56 times

by raunekk » Mon Nov 03, 2008 11:15 pm

using pythagoras theorem..
u will b able to find line segment BC
and similarly AB
Let AC=x

Thus BC=root of( x^2 + x^2 ) + x^2 = x root3=1.732x
AB= root of( x^2 + x^2 ) = x root2=1.414x

Thus BC- AB = 0.318x

i.e 0.318x/ x * 100 = 30% (approx.)

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Lakers09: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Nov 02, 2008 5:49 pm

by Lakers09 » Tue Nov 04, 2008 11:11 am

I feel like an idiot. I understand pythag theorem. Maybe I am forgetting some rules about simplifying radicals and exponents? any suiggestions?

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elmiko: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue Sep 16, 2008 3:22 pm

by elmiko » Tue Nov 04, 2008 3:23 pm

raunekk wrote:
Thus BC=root of( x^2 + x^2 ) + x^2 = x root3=1.732x
AB= root of( x^2 + x^2 ) = x root2=1.414x

I must have forgotten this rule of roots/exponents.

What is/are the rule/s for taking the square root of numbers with exponents?

I know that the general rule in simplifying the z'th root of (x^n) = x^n/z.
i.e. cubed root (x^2) = x^2/3.

How do you simplify when there is more than 1 term within a square root?

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kanishkporwal: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Sep 14, 2011 9:56 pm

by kanishkporwal » Fri Sep 16, 2011 10:00 pm

Lakers09 wrote:I feel like an idiot. I understand pythag theorem. Maybe I am forgetting some rules about simplifying radicals and exponents? any suiggestions?

If you are forgetting the basics on radical simplification then you should definitely check this link

https://math.tutorvista.com/number-syste ... icals.html

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