If A=10+3-10-3 10-1, B=3+22, What is A - B?

Question

If  A=\frac{\sqrt{\sqrt{10}+3}-\sqrt{\sqrt{10}-3}}{\sqrt{\sqrt{10}-1}} , and  B=\sqrt{3+2\sqrt{2}} , what is the value of  A - B ?

A.  -2  
 
B.  -1 
 
C.  0 
 
D.  1 
 
E.  2

gmatophobia · Accepted Answer

Let's start by simplifying the terms -

B=\sqrt{3+2\sqrt{2}}

B=\sqrt{(1+\sqrt{2})^2}

B=1 +\sqrt{2}

A=\frac{\sqrt{\sqrt{10}+3}-\sqrt{\sqrt{10}-3}}{\sqrt{\sqrt{10}-1}}

Squaring on both sides of the equation we get

A^2=\frac{(\sqrt{\sqrt{10}+3})^2+(\sqrt{\sqrt{10}-3})^2 - 2(\sqrt{(\sqrt{10}-3)(\sqrt{10}+3)})}{(\sqrt{\sqrt{10}-1})^2}

A^2=2

A=\sqrt{2}

A - B = \sqrt{2} - (1 +\sqrt{2}) = -1

Option B

The detailed work is shown in the attached image

Regor60 · Answer

It's probably quicker to estimate rather than perform the necessary algebra to determine the exact answer.

A: √10 is 3.x, so the numerator is ~√6-0. The denominator is ~√2, so

A = ~√3 or ~1.7

B: Since √2=~1.4,

B = ~√6 = √2*√3 = 1.4*1.7
 =2.4

So A-B =~-.7 = ~-1

Adidas1424 · Answer

Regor60 · Answer

The right side under the larger root is √10-3.

Since √10 is a little larger than 3, the right side is approximately:

√(~3-3) = √0

And the left side, since it ADDS 3 to the √10 is therefore approximately √6

To be clear this estimation works only because the answer choices are far apart, since we're reducing the right side to 0 where the actual result is close to .4

If A=10+3-10-3 10-1, B=3+22, What is A - B?

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If A=10+3-10-3 10-1, B=3+22, What is A - B?

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