sqr root * exponents

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mikeclarke44: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Jun 09, 2007 11:57 am

sqr root * exponents

by mikeclarke44 » Fri Jun 15, 2007 7:32 am

I seem to be close on this one but something in my math seems off.

Of the following integers which is the closest approx to (sqr root 2 + sqr root 5)^2

a) 7
b) 10
c) 13
d) 15
e) 17

I get (SR 2 + SR 5)(SR 2 + SR 5)
2 + SR10 + SR10 + 5
7 + SR20
7 + SR4 + SR 5
9 + SR5
Which probabily 11+ a little bit more. The answer is (c), but is my math right?

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Source: Beat The GMAT — Problem Solving | Fri Jun 15, 2007 7:32 am

Neo2000: Legendary Member; Posts: 519; Joined: Sat Jan 27, 2007 7:56 am; Location: India; Thanked: 31 times

Re: sqr root * exponents

by Neo2000 » Fri Jun 15, 2007 9:36 am

mikeclarke44 wrote:I seem to be close on this one but something in my math seems off.

I get (SR 2 + SR 5)(SR 2 + SR 5)
2 + SR10 + SR10 + 5
7 + SR20
7 + SR4 + SR 5
9 + SR5
Which probabily 11+ a little bit more. The answer is (c), but is my math right?

SR10 + SR10 = 2SR10 = SR40

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mikeclarke44: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Jun 09, 2007 11:57 am

by mikeclarke44 » Fri Jun 15, 2007 10:45 am

Still not following you.
I understand that SR10 + SR10 = 2SR10
but you lost me when you said 2SR10 = SR40

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thumpin_termis: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Fri Jun 01, 2007 11:02 pm

by thumpin_termis » Fri Jun 15, 2007 1:59 pm

mikeclarke44 wrote:but you lost me when you said 2SR10 = SR40

2SR10 = SR(4*10) = SR40

If don't get that, then check this link out and review working with square roots.

https://www.purplemath.com/modules/radicals.htm

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mikeclarke44: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Jun 09, 2007 11:57 am

by mikeclarke44 » Fri Jun 15, 2007 10:37 pm

Thanks, that does help!

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moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

Well..

by moneyman » Sat Jun 16, 2007 8:59 am

(Sq.root 2+Sq.root5)^2 is in the format of (a+b)^2

(a+b)^2 is a^2+2ab+b^2

Substitute the values in the formula and you will get

(Sq.rt 2)^2+2(Sq.rt2)(Sq.rt5)+(Sq.rt5)^2

The result is 2+2(Sq.rt 10)+5 which is 7+2(sq.rt10)

Sq.rt 9 is 3 ,so sq.rt 10 should be somewhere around 3.1 or 3.2 and so

7+2(3.1) would be close to answer choice C

Maxx

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vmahalin: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Jun 19, 2007 6:10 am

by vmahalin » Tue Jun 19, 2007 11:43 am

This is how it goes,

(sq2 + sq5)^2 = (sq2)^2 + (sq5)^2 + 2 x (sq2) x (sq5)

[apply formula (a+b)^2]

= 2 + 5 + 2(sq 10)

Now the question is "value closest to", instead of sq10 assume sq9.
sq9 is 3.

= 7 + 2(sq9) = 7 + (2 x 3) = 13.

Hence the answer is 13.