If a b 0, then √a^2 - b^2

Question

If a > b > 0, then  \sqrt{a^2 - b^2}

A.  a + b - \sqrt{2ab}

B.  a - b + \sqrt{2ab}

C.  \sqrt{(a-b)^2 - 2ab}

D.  (\sqrt{a+b}) (\sqrt{a-b})

E.  (\sqrt{a} + \sqrt{b}) (\sqrt{a}-\sqrt{b})

What is the difference between D and E

I thought because of the numbers being all under the square root e.g. in D  (\sqrt{a+b})  
that you will have to subtract a from b first giving e.g. answer \sqrt{c}  and for the other one e.g. \sqrt{d}

And therefore  (\sqrt{c})(\sqrt{d})  a totally different value?

Bunuel · Accepted Answer

a^2 - b^2 = (a + b)(a - b) , thus  \sqrt{a^2 - b^2}=\sqrt{(a + b)(a - b)} , which is the same as  \sqrt{(a + b)}\sqrt{(a - b)} .

Answer: D.

Jeli13 · Answer

mmhh ok seem to have overcomplicated my thoughts

BuggerinOn · Answer

I picked numbers for this question, a = 2 and b = 1 yields  \sqrt{3}  and the only answer choice that yields  \sqrt{3}  when substituting a for 2 and b for 1 is D.

SVaidyaraman · Answer

Main Idea: Identify that a formula can be used

Details We see that root(a^2 - b^2) is nothing by root((a+b) (a-b))= root(a+b)*root(a-b)

Hence D.

JeffTargetTestPrep · Answer

Notice that (a^2 - b^2) is a difference of squares, which we can factor. Simplifying the given expression, we have:

√(a^2 - b^2) = √(a +b)(a - b) = √(a + b) x √(a - b)

Answer: D

nfarmer · Answer

You clearly got it right, but aren't "a" and "b" supposed to be negative?

AnirudhaS · Answer

\sqrt{a^2-b^2} 
= \sqrt{(a+b)(a-b)} 
= \sqrt{a+b} \sqrt{a-b}

Answer:  D

MathRevolution · Answer

\sqrt{6} = \sqrt{2*3} = \sqrt{2} * \sqrt{3}

Similarly,  \sqrt{a^2 - b^2} = \sqrt{(a - b)(a + b)} = \sqrt{a - b}\sqrt{a + b}

Answer D

Crytiocanalyst · Answer

a^2 -b^2= a+b*a-b
if square root is taken '

Then we get \/a+b*a-b

if there is any confusion then plugging in should do the trick 
let a=2 and b=1 
then we get only D as the right option therefore IMO D

ablatt4 · Answer

If a = 3 and b = 2

plug into original expression and get sqrt 5

plug the same x and y values into each and see which gives you sqrt 5

D

If a > b > 0, then √a^2 - b^2

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