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

Question

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

Bunuel · Accepted Answer

MAGOOSH OFFICIAL SOLUTION: rootaplusrootb_text.png

AmoyV · Answer

16^2 =256

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

a-b=5

Answer: E

a+b=17
a= \frac{66}{b}

Lucky2783 · Answer

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

Answer 5. E.

PareshGmat · Answer

Answer = E = 5

\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

lipsi18 · Answer

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

Hence answer is E

Harley1980 · Answer

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

So answer is E

sahilvijay · Answer

Answer is E 
see pic for details

rahul16singh28 · Answer

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

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

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

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