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Challenge - Radical Exponents (m06q20) [#permalink]
 12 Nov 2007, 09:11
Question Stats:
52% (01:06) correct
48% (00:25) wrong based on 1 sessions
The square of 5^{\sqrt{2}} = ? (A) 5^2(B) 25^{\sqrt{2}}(C) 25(D) 25^{2\sqrt{2}}(E) 5^{\sqrt{2}^2} Source: GMAT Club Tests - hardest GMAT questions Can someone please explain the answer?
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square of 5^(root2)=
(5^(root2)^2==
5^(root2)^2
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Re: Challenge - Radical Exponents [#permalink]
12 Nov 2007, 11:13
bmwhype2 wrote: The square of 5^sqrt(2) is
5^2
25^sqrt(2)
25
25^2sqrt(2)
5^sqrt(2)^2
Can someone please explain the answer?
I'm getting B.
[5^sqrt(2)]^2 = (5^2)^sqrt(2) = 25^sqrt(2)
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I couldn't find the answer in the given stem.
9.75 is caculated value and none of the answer has that output
5^2 = 25
25^sqrt(2) = 94.77
25
25^2sqrt(2) = 46.08
5^sqrt(2)^2 = 25
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I get 5^2
I tried substituting 4 for 2 - (5^sqrt4) x (5^sqrt4)
5^sqrt4 = 5^2 = 25 - so 25 x 25 = 625 = 5^4
On that basis I'd say (5^sqrt2) x (5^sqrt2) = 5^2
Anyone with views?
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Manager
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i agree with priyankur, could there be a typo?
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Re: Challenge - Radical Exponents [#permalink]
13 Nov 2007, 11:43
bmwhype2 wrote: The square of 5^sqrt(2) is
5^2
25^sqrt(2)
25
25^2sqrt(2)
5^sqrt(2)^2
Can someone please explain the answer?
I get B, 25^sqrt(2)
When an exponent is raised to another exponent, they are multiplied. Thus,
The square of 5^sqrt(2) = 5^(2*sqrt(2)), then calculating backwards,
5^(2*sqrt(2)) also equals [5^(2)]^sqrt(2) = [25]^sqrt(2)
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priyankur just to let u knwo i figured out what we did wrong. we didnt square the original statement
5^(sqrt2) = 9.738 but then we have to square that to get 94.838
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
22 Dec 2009, 02:39
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
27 May 2010, 07:59
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5^\sqrt{2} x 5^\sqrt{2} => 5^\sqrt{2}+\sqrt{2} => 5^2\sqrt{2} = 25^\sqrt{2} B is correct.
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
27 May 2010, 13:54
The square of 5^sqrt(2) is
5^2
25^sqrt(2)
25
25^2sqrt(2)
5^sqrt(2)^2
Can someone please explain the answer?
B is the answer
[5^sqrt(2)]^2 = 25^2sqrt(2)
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
27 May 2010, 23:49
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Here's a quote from the thread mentioned above: Quote: Tania, consider these examples:
(5^1)^2 = 5^2 = 25 --> the answer is 5^2, not 25^2, which would equal 5^4 (incorrect).
(5^2)^2 = 5^{2*2} = 5^4 = 625 = 25^2 --> You see that we had to multiply the exponents (2*2) but didn't change the base at that stage yet. If we follow your logic we end up with 25^{2*2}, which is not right since we've squared the expression 5^2 twice, not once (we squared the base and multiplied the exponent by 2).
Let's see our problem again:
(5^{\sqrt{2}})^2 = 5^{2\sqrt{2}} = (5^2)^{\sqrt{2}} = 25^{\sqrt{2}} --> make sure you square the expression once
So, the right answer could be either 25^{\sqrt{2}} or 5^{2\sqrt{2}}. I hope it helped make it a bit clearer.
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
28 May 2010, 03:06
Answer is 25^root2
2^2^3 is same as 4^3
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
28 May 2010, 03:52
Yes, the answer is B. However, your statement in red is not correct. 2^{2^3} = 2^8 = 2564^3 = 64If you meant to type 2^{2*3} is same as 4^3, then you're correct. ameyaberi wrote: Answer is 25^root2
2^2^3 is same as 4^3
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
06 Aug 2010, 06:36
(5^sqrt2)^2 = 5^2^1/2*2^1....since same base we have to add the exponents
= 5^2^3/2
= 5^sqrt2^3
= 5^2*sqrt2
= 25^sqrt2...Thus B
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
31 May 2011, 05:06
5^(root(2)) * 5^(root(2)) = 5^2(root(2)) = 25^(root(2)) Answer - B
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
31 May 2011, 08:50
answer is B
(a^m)^n = a^mn = (a^n)^m
hence
(5^sqrt2)^2 = 5^sqrt2*2 = (5^2)^sqrt2 = 25^sqrt2
hope that helps.
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
01 Jun 2011, 06:47
I get the following results.
Attachments
explantionfor5root.JPG [ 17.97 KiB | Viewed 2442 times ]
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
01 Jun 2011, 07:19
As it was correctly stated by abcg27 (you can see the quote below), you've taken the same path. If you go one step further, you'll arrive at B: 5^{2\sqrt{2}} = (5^2)^{\sqrt{2}} = 25^{\sqrt{2}}abcg27 wrote: answer is B
(a^m)^n = a^mn = (a^n)^m
hence
(5^sqrt2)^2 = 5^sqrt2*2 = (5^2)^sqrt2 = 25^sqrt2
hope that helps. toughmat wrote: I get the following results.
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Re: Challenge - Radical Exponents (m06q20) [#permalink]
01 Jun 2011, 07:25
toughmat wrote: I get the following results.  ^^ what you did so far is correct. Further to match with the given choices, split 5^2*\sqrt{^2} as (5^2)\sqrt{^2} = (25)\sqrt{^2}, which is given in choices
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Re: Challenge - Radical Exponents (m06q20)
[#permalink]
01 Jun 2011, 07:25
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