Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 02:21 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56267
If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

1
19 00:00

Difficulty:   65% (hard)

Question Stats: 59% (02:15) correct 41% (02:30) wrong based on 243 sessions

### HideShow timer Statistics If $$\sqrt{17+\sqrt{264}}$$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =

A. 1
B. 2
C. 3
D. 4
E. 5

Kudos for a correct solution.

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56267
Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

3
7
Bunuel wrote:
If $$\sqrt{17+\sqrt{264}}$$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =

A. 1
B. 2
C. 3
D. 4
E. 5

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment: rootaplusrootb_text.png [ 12.94 KiB | Viewed 7197 times ]

_________________
##### General Discussion
Retired Moderator B
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 304
Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

2
Bunuel wrote:
If $$\sqrt{17+\sqrt{264}}$$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =

A. 1
B. 2
C. 3
D. 4
E. 5

Kudos for a correct solution.

$$16^2$$=256

17+2$$\sqrt{66}$$=a+b+2$$\sqrt{ab}$$
b=6 a=11

a-b=5

a+b=17
a=$$\frac{66}{b}$$
Director  Joined: 07 Aug 2011
Posts: 518
GMAT 1: 630 Q49 V27 If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

2
1
Bunuel wrote:
If $$\sqrt{17+\sqrt{264}}$$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =

A. 1
B. 2
C. 3
D. 4
E. 5

Kudos for a correct solution.

IF $$\sqrt{17+\sqrt{264}}$$ = $$\sqrt{a}+\sqrt{b}$$ THEN
$$17+ \sqrt{264} = a + b +2 \sqrt{ab}$$
$$17+2 * \sqrt{66} = a + b +2 \sqrt{ab}$$
implying that b=6 and a=11

SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

1

$$\sqrt{17+\sqrt{264}} = \sqrt{a}+\sqrt{b}$$

$$17 + \sqrt{264} = a + 2\sqrt{ab} + b$$

$$11 + 2\sqrt{11*6} + 6 = a + 2\sqrt{ab} + b$$

LHS & RHS are similar

a-b = 11-6 = 5
_________________
Kindly press "+1 Kudos" to appreciate Manager  B
Joined: 26 Dec 2012
Posts: 145
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

We can write mentioned equation as; 17+root 264 = (root a+root b)^2= a+b+2 root a*b
Therefore, a+b=17 & 2 root a*b=root 264; square both side we can get value of a*b = 66;
Using above data we can find out a-b; by entering values in (a-b)^2 =(a+b)^2-4ab we get (a-b) =5

Retired Moderator Joined: 06 Jul 2014
Posts: 1224
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

2
1
Bunuel wrote:
If $$\sqrt{17+\sqrt{264}}$$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =

A. 1
B. 2
C. 3
D. 4
E. 5

Kudos for a correct solution.

At first we see that we can't calculate result of this expression $$\sqrt{17+\sqrt{264}}$$
So we should eliminate the root by powering equation
$$(\sqrt{17+\sqrt{264}})^2=(\sqrt{a}+\sqrt{b})^2$$
$$17+\sqrt{264}=a + 2sqrt{ab}+b$$

And now we should try to express first part of equation in the form of second equation. As we have 2 before root in right side of equation, we should extract 2 from root in left side of equation:
$$\sqrt{264}=\sqrt{4 * 66}=2\sqrt{66}$$

And as a final step we should find roots for equations $$ab=66$$ and $$a+b=17$$ this is 6 and 11
And we can write our equation in symmetric view:
$$11+2\sqrt{11*6}+6=a + 2sqrt{ab}+b$$
$$a - b = 11 - 6 = 5$$

_________________
Senior Manager  P
Joined: 29 Jun 2017
Posts: 448
GPA: 4
WE: Engineering (Transportation)
Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

see pic for details
Attachments IMG_9053.JPG [ 834.87 KiB | Viewed 4128 times ]

_________________
Give Kudos for correct answer and/or if you like the solution.
Director  P
Joined: 31 Jul 2017
Posts: 515
Location: Malaysia
GMAT 1: 700 Q50 V33 GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  [#permalink]

### Show Tags

Bunuel wrote:
If $$\sqrt{17+\sqrt{264}}$$ can be written in the form $$\sqrt{a}+\sqrt{b}$$ , where a and b are integers and b < a, then a - b =

A. 1
B. 2
C. 3
D. 4
E. 5

Kudos for a correct solution.

The equation can be written as -

$$\sqrt{17+\sqrt{264}}$$ = $$\sqrt{a}+\sqrt{b}$$

Squaring on both Sides we get -

a + b = 17, ab = 66

Hence a = 11, b = 6.

a - b = 5
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Re: If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,   [#permalink] 23 Nov 2018, 02:30
Display posts from previous: Sort by

# If \sqrt{17+\sqrt{264}} can be written in the form \sqrt{a}+\sqrt{b} ,  