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Hard Radical question

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CEO
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Hard Radical question [#permalink] New post 28 Oct 2007, 19:59
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach
VP
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Re: Hard Radical question [#permalink] New post 28 Oct 2007, 20:02
bmwhype2 wrote:
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach


sqrt (7 + sqrt(48)) - sqrt(3)

sqrt (7 + 4*sqrt(3)) - sqrt(3)

sqrt (7 + 3*sqrt(3))

= appx 3 ..So E
CEO
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Re: Hard Radical question [#permalink] New post 28 Oct 2007, 20:14
bmwhype2 wrote:
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach


I get E as well. Actually my answer is bigger than E. I guess im kinda confused with the way the problem is typed.

is the -sqrt(3) under the same sqrt as the 7?
VP
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Re: Hard Radical question [#permalink] New post 28 Oct 2007, 20:21
GMATBLACKBELT wrote:
bmwhype2 wrote:
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach


I get E as well. Actually my answer is bigger than E. I guess im kinda confused with the way the problem is typed.

is the -sqrt(3) under the same sqrt as the 7?


Fantastic question the answer is 2

Here it is

sqrt (7 + sqrt(48)) - sqrt(3)

Conside the bolded part

the square root is sqrt(4) + sqrt(3)

Not subtracting -sqrt(3) we get sqrt(4) remaining which is 2
CEO
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Re: Hard Radical question [#permalink] New post 28 Oct 2007, 20:29
trivikram wrote:
GMATBLACKBELT wrote:
bmwhype2 wrote:
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach


I get E as well. Actually my answer is bigger than E. I guess im kinda confused with the way the problem is typed.

is the -sqrt(3) under the same sqrt as the 7?


Fantastic question the answer is 2

Here it is

sqrt (7 + sqrt(48)) - sqrt(3)

Conside the bolded part

the square root is sqrt(4) + sqrt(3)

Not subtracting -sqrt(3) we get sqrt(4) remaining which is 2


Ok now I see, yes agree w/ 2. sqrt7+4sqrt3 ~ sqrt13.8~3.7 -1.7= 2.
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Re: Hard Radical question [#permalink] New post 28 Oct 2007, 21:43
trivikram wrote:
GMATBLACKBELT wrote:
bmwhype2 wrote:
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach


I get E as well. Actually my answer is bigger than E. I guess im kinda confused with the way the problem is typed.

is the -sqrt(3) under the same sqrt as the 7?


Fantastic question the answer is 2

Here it is

sqrt (7 + sqrt(48)) - sqrt(3)

Conside the bolded part

the square root is sqrt(4) + sqrt(3)

Not subtracting -sqrt(3) we get sqrt(4) remaining which is 2


good one "trivikram".

= sqrt (7 + sqrt(48)) - sqrt(3)
= sqrt (4 + 2 sqrt(12) + 3) - sqrt(3)
= sqrt ((2)^2 + 2 (2) sqrt (3) + sqrt(3)^2 - sqrt(3)
= sqrt [{(2)^2 + sqrt (3)}^2] - sqrt(3)
= 2 + sqrt (3) - sqrt(3)
= 2
Director
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Re: Hard Radical question [#permalink] New post 28 Oct 2007, 22:26
bmwhype2 wrote:
sqrt (7 + sqrt(48)) - sqrt(3)?

1
1.7
2.0
2.4
3.0

Please explain your approach


2.

sqrt (48) = 4sqrt(3)

7+4sqrt(3) = (2+3sqrt(2))^2

Question becomes

2 + sqrt(3) - sqrt(3) = ?

Answer = 2.
Re: Hard Radical question   [#permalink] 28 Oct 2007, 22:26
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