Author
Message
CEO

Joined: 21 Jan 2007

Posts: 2775

Location: New York City

Followers: 6

Kudos [? ]:
170
[0 ] , given: 4

Challenge - Radical Exponents (m06q20) [#permalink ]
12 Nov 2007, 08:11

Question Stats:

59% (01:21) correct

40% (00:29) wrong

based on 169 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

SOLUTION: challenge-radical-exponents-m06q20-55442-20.html#p1232318

Senior Manager

Joined: 01 Sep 2006

Posts: 302

Location: Phoenix, AZ, USA

Followers: 1

Kudos [? ]:
9
[0 ] , given: 0

square of 5^(root2)=
(5^(root2)^2==
5^(root2)^2

Director

Joined: 09 Aug 2006

Posts: 770

Followers: 1

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

Re: Challenge - Radical Exponents [#permalink ]
12 Nov 2007, 10:13

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)

Director

Joined: 25 Oct 2006

Posts: 652

Followers: 7

Kudos [? ]:
153
[0 ] , given: 6

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

Manager

Joined: 08 Nov 2007

Posts: 100

Followers: 1

Kudos [? ]:
1
[0 ] , given: 0

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?

Current Student

Joined: 18 Jun 2007

Posts: 408

Location: Atlanta, GA

Schools: Emory class of 2010

Followers: 10

Kudos [? ]:
33
[0 ] , given: 0

Re: Challenge - Radical Exponents [#permalink ]
13 Nov 2007, 10:43

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)

Manager

Joined: 19 Aug 2007

Posts: 169

Followers: 1

Kudos [? ]:
6
[0 ] , given: 0

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

CIO

Joined: 02 Oct 2007

Posts: 1218

Followers: 85

Kudos [? ]:
597
[0 ] , given: 334

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
22 Dec 2009, 01:39

Director

Joined: 21 Dec 2009

Posts: 588

Concentration: Entrepreneurship, Finance

Followers: 15

Kudos [? ]:
201
[3 ] , given: 20

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
27 May 2010, 06:59
3

This post receivedKUDOS

5^\sqrt{2} x 5^\sqrt{2}

=> 5^\sqrt{2}+\sqrt{2}

=> 5^2\sqrt{2}

= 25^\sqrt{2}

B is correct.

_________________

KUDOS me if you feel my contribution has helped you.

Intern

Joined: 27 May 2010

Posts: 1

Followers: 0

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

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
27 May 2010, 12:54

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)

CIO

Joined: 02 Oct 2007

Posts: 1218

Followers: 85

Kudos [? ]:
597
[4 ] , given: 334

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
27 May 2010, 22:49
4

This post receivedKUDOS

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.

_________________

Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Intern

Joined: 27 May 2010

Posts: 6

Followers: 0

Kudos [? ]:
20
[0 ] , given: 0

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
28 May 2010, 02:06

Answer is 25^root2 2^2^3 is same as 4^3

CIO

Joined: 02 Oct 2007

Posts: 1218

Followers: 85

Kudos [? ]:
597
[0 ] , given: 334

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
28 May 2010, 02:52

Yes, the answer is B. However, your statement in red is not correct.

2^{2^3} = 2^8 = 256 4^3 = 64 If you meant to type

2^{2*3} is same as

4^3 , then you're correct.

ameyaberi wrote:

Answer is 25^root22^2^3 is same as 4^3

_________________

Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Intern

Joined: 03 Aug 2010

Posts: 2

Followers: 0

Kudos [? ]:
1
[0 ] , given: 0

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
06 Aug 2010, 05:36

(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

SVP

Joined: 16 Nov 2010

Posts: 1698

Location: United States (IN)

Concentration: Strategy, Technology

Followers: 29

Kudos [? ]:
263
[0 ] , given: 36

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
31 May 2011, 04:06

5^(root(2)) * 5^(root(2)) = 5^2(root(2)) = 25^(root(2))

Answer - B

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Intern

Joined: 29 May 2011

Posts: 1

Followers: 0

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

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
31 May 2011, 07:50

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.

Manager

Joined: 19 Apr 2011

Posts: 112

Followers: 2

Kudos [? ]:
3
[0 ] , given: 2

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
01 Jun 2011, 05:47

I get the following results.

Attachments

explantionfor5root.JPG [ 17.97 KiB | Viewed 4786 times ]

CIO

Joined: 02 Oct 2007

Posts: 1218

Followers: 85

Kudos [? ]:
597
[0 ] , given: 334

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
01 Jun 2011, 06:19

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.

_________________

Welcome to GMAT Club! Want to solve GMAT questions on the go? GMAT Club iPhone app will help. Please read this before posting in GMAT Club Tests forum Result correlation between real GMAT and GMAT Club Tests Are GMAT Club Test sets ordered in any way? Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Intern

Joined: 24 May 2010

Posts: 47

Followers: 0

Kudos [? ]:
5
[0 ] , given: 6

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
01 Jun 2011, 06:25

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

Intern

Joined: 20 Apr 2011

Posts: 45

Location: United Kingdom

Followers: 0

Kudos [? ]:
0
[0 ] , given: 9

Re: Challenge - Radical Exponents (m06q20) [#permalink ]
10 Jun 2011, 03:18

(a^x)^m = (a^m)^x (5^[square_root]2)^2 = (5^2)^[square_root]2 = 25^[square_root]2

Re: Challenge - Radical Exponents (m06q20)
[#permalink ]
10 Jun 2011, 03:18