What is the value of 404^2 - 396^2 ?

Question

What is the value of  \sqrt{404^2 - 396^2}  ?

(A) 60

(B) 80

(C) 90

(D) 120

(E) 144

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Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=cmpDVLHzT3w

Reon · Answer

(404)^2 -(396)^2 
(400+4)^2 - (400-4)^2 
(400)^2 +(4)^2 +2(400)(4) - ((400)^2 +(4)^2 -2(400)(4))
3200 + 3200
6400

(6400)^1/2 =80

B

MarkGMATMentor · Answer

One squared quantity minus another squared quantity is a signal that you should use the difference of squares identity:

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

In this case, the original expression  \sqrt{404^2 - 396^2}   becomes:

\sqrt{(404 + 396)(404 - 396)}

Then simplify:

\sqrt{(800)(8)}

\sqrt{6400}

80

The answer is B.

Note that in some cases, it's also helpful to go the other direction in the difference of squares identity rather than add/subtract within the parentheses. For example:

(100 + 9)(100 - 9) ---> 10,000 - 81 ---> 9,919

Always look out for the difference of squares. The GMAT frequently likes to include this identity when it tests algebraic concepts.

vasu1104 · Answer

\sqrt{404^2-396^2} 
 
here we can use a^2- b^2 = (a-b)(a+b)

√(404−396)(404+396)
 (8)(800)
6400

taking square root of it gives = 8*10= 80

choice B

TheAdmissionHub · Answer

This exercise can be solved using the  difference of squares :  (a^2-b^2)=(a+b)*(a-b)

\sqrt{404^2-396^2} =    \sqrt{(404+396)*(404-396)} =    \sqrt{800*8}   = \sqrt{6400 }= 80

Answer: B

What is the value of 404^2 - 396^2 ?

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What is the value of 404^2 - 396^2 ?

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