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# Exponents, Radicals, & More

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Senior Manager
Joined: 02 Nov 2008
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Exponents, Radicals, & More [#permalink]

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16 Nov 2009, 20:53
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100% (01:39) correct 0% (00:00) wrong based on 6 sessions

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(sqrt(9 +sqrt80) + sqrt(9-sqrt80))^2
The square root of the sum of 9 and the square root of 80 plus the square root difference (so subtraction) between 9 and the square root of 80 (so the 9’s are under one radical (initial square root) and the 80’s are under 2 radicals.
a) 1
b) 9 – 4(5)^1/2
c) 14
d) 18
e) 20

Last edited by chicagocubsrule on 17 Nov 2009, 15:10, edited 1 time in total.
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 261 [0], given: 31

Re: Exponents, Radicals, & More [#permalink]

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16 Nov 2009, 21:21
chicagocubsrule wrote:
((9^(1/2) +80^(1/4)) +(9^(1/2) – 80^(1/4)) ^2
The square root of the sum of 9 and the square root of 80 plus the square root difference (so subtraction) between 9 and the square root of 80 (so the 9’s are under one radical (initial square root) and the 80’s are under 2 radicals.
a) 1
b) 9 – 4(5)^1/2
c) 14
d) 18
e) 20

I keep getting 36..are you sure this is correct?

I double-checked with google calculator and it too got 36

http://www.google.com/#hl=en&q=((9^(1%2F2)+%2B+80^(1%2F4))%2B(9^(1%2F2)+-+80^(1%2F4)))^2&aq=f&aqi=&oq=&fp=1c443ffcb5a5cce1
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 261 [0], given: 31

Re: Exponents, Radicals, & More [#permalink]

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17 Nov 2009, 06:23
chicagocubsrule wrote:
((9^(1/2) +80^(1/4)) +(9^(1/2) – 80^(1/4)) ^2
The square root of the sum of 9 and the square root of 80 plus the square root difference (so subtraction) between 9 and the square root of 80 (so the 9’s are under one radical (initial square root) and the 80’s are under 2 radicals.
a) 1
b) 9 – 4(5)^1/2
c) 14
d) 18
e) 20

answer 20

but question should read (sqrt(9 +sqrt80) + sqrt(9-sqrt80))^2
Senior Manager
Joined: 02 Nov 2008
Posts: 282
Followers: 1

Kudos [?]: 99 [0], given: 2

Re: Exponents, Radicals, & More [#permalink]

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17 Nov 2009, 15:09
lagomez wrote:
chicagocubsrule wrote:
((9^(1/2) +80^(1/4)) +(9^(1/2) – 80^(1/4)) ^2
The square root of the sum of 9 and the square root of 80 plus the square root difference (so subtraction) between 9 and the square root of 80 (so the 9’s are under one radical (initial square root) and the 80’s are under 2 radicals.
a) 1
b) 9 – 4(5)^1/2
c) 14
d) 18
e) 20

answer 20

but question should read (sqrt(9 +sqrt80) + sqrt(9-sqrt80))^2

my mistake (I've edited my original post)...answer is 20...can you please explain?
VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 261 [0], given: 31

Re: Exponents, Radicals, & More [#permalink]

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17 Nov 2009, 15:42
chicagocubsrule wrote:
lagomez wrote:
chicagocubsrule wrote:
((9^(1/2) +80^(1/4)) +(9^(1/2) – 80^(1/4)) ^2
The square root of the sum of 9 and the square root of 80 plus the square root difference (so subtraction) between 9 and the square root of 80 (so the 9’s are under one radical (initial square root) and the 80’s are under 2 radicals.
a) 1
b) 9 – 4(5)^1/2
c) 14
d) 18
e) 20

answer 20

but question should read (sqrt(9 +sqrt80) + sqrt(9-sqrt80))^2

think of (a+b)^2 = a^2 + 2ab + b^2

let's say a = sqrt(9 + sqrt80)
so that squared = 9 + sqrt 80

b = sqrt(9-sqrt80) and that squared = 9 - sqrt 80

2ab
= 2(sqrt(9+sqrt80)*sqrt(9-sqrt80)
=2((9+sqrt80)(9-sqrt80))
=2(81+80)
=2(1)
=2

combing all we get:
9 +sqrt80 + 9 - sqrt80 + 2 = 20
Senior Manager
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Re: Exponents, Radicals, & More [#permalink]

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17 Nov 2009, 15:51
chicagocubsrule wrote:
(sqrt(9 +sqrt80) + sqrt(9-sqrt80))^2
The square root of the sum of 9 and the square root of 80 plus the square root difference (so subtraction) between 9 and the square root of 80 (so the 9’s are under one radical (initial square root) and the 80’s are under 2 radicals.
a) 1
b) 9 – 4(5)^1/2
c) 14
d) 18
e) 20

Chicago - it would be easier to read if u use "m"

questions-about-posting-84537.html#p636437

reading the question itself took half of my energy - LOL

BTW I got 20 too

here we are applying the formulas
$$(a+b)^2 = a^2+2ab+b^2$$
and
$$(a+b)(a-b) = a^2-b^2$$
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Re: Exponents, Radicals, & More   [#permalink] 17 Nov 2009, 15:51
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# Exponents, Radicals, & More

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