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Sub 505 (Easy)|   Algebra|         
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Bunuel
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What is the value of 404^2 - 396^2 ? 22 Jun 2026, 19:00
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B
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5% (low)

Question Stats:

90% (01:21) correct 10% (02:21) wrong based on 111 sessions

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

(A) 60

(B) 80

(C) 90

(D) 120

(E) 144

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B
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Bunuel
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What is the value of 404^2 - 396^2 ? 27 Jun 2026, 03:00
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Bunuel
What is the value of \(\sqrt{404^2 - 396^2}\) ?

(A) 60

(B) 80

(C) 90

(D) 120

(E) 144
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Reon
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What is the value of 404^2 - 396^2 ? 22 Jun 2026, 19:23
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(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
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GMAT 1: 790 Q51 V50
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What is the value of 404^2 - 396^2 ? 22 Jun 2026, 20:18
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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.
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What is the value of 404^2 - 396^2 ? 22 Jun 2026, 22:49
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[ltr]\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

[/ltr]


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

(A) 60

(B) 80

(C) 90

(D) 120

(E) 144

This is a PS Butler Question

Check the links to other Butler Projects:

­
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What is the value of 404^2 - 396^2 ? 27 Jun 2026, 09:36
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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
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