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# (4 + 5^1/2) (4 – 5^1/2) is equal to:?

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(4 + 5^1/2) (4 – 5^1/2) is equal to:?  [#permalink]

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14 Dec 2019, 04:39
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Difficulty:

5% (low)

Question Stats:

91% (00:24) correct 9% (00:25) wrong based on 44 sessions

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$$(4 + \sqrt{5}) (4 – \sqrt{5})$$ is equal to:

(A) –1
(B) 0
(C) 11
(D) 21
(E) 11 + 8 $$\sqrt{5}$$

Source: Master GMAT

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Posts: 8626
Re: (4 + 5^1/2) (4 – 5^1/2) is equal to:?  [#permalink]

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14 Dec 2019, 04:43
$$(4 + \sqrt{5}) (4 – \sqrt{5})$$ is equal to:

(A) –1
(B) 0
(C) 11
(D) 21
(E) 11 + 8 $$\sqrt{5}$$

Source: Master GMAT

Whenever you are looking at something similar to (a-b)(a+b), the answer is $$a^2-b^2$$
So $$4^2-\sqrt{5}^2=16-5=11$$

C
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Re: (4 + 5^1/2) (4 – 5^1/2) is equal to:?  [#permalink]

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14 Dec 2019, 09:48
$$(4 + \sqrt{5}) (4 – \sqrt{5})$$ is equal to:

(A) –1
(B) 0
(C) 11 --> correct: $$(4 + \sqrt{5}) (4 – \sqrt{5})$$ = $$(4^2 - \sqrt{5}^2)$$ = 16-5=11
(D) 21
(E) 11 + 8 $$\sqrt{5}$$
Senior Manager
Joined: 30 Oct 2019
Posts: 383
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4
(4 + 5^1/2) (4 – 5^1/2) is equal to:?  [#permalink]

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14 Dec 2019, 10:06
Its in $$a^2 - b^2$$ form.

Putting the numbers in: $$4^2 -(\sqrt{5})^2$$ = 16-5 = 11

Ans: C
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Joined: 17 Jan 2018
Posts: 99
Concentration: Entrepreneurship, Strategy
Re: (4 + 5^1/2) (4 – 5^1/2) is equal to:?  [#permalink]

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15 Dec 2019, 04:06
$$(4 + \sqrt{5}) (4 – \sqrt{5})$$ is equal to:

(A) –1
(B) 0
(C) 11
(D) 21
(E) 11 + 8 $$\sqrt{5}$$

Source: Master GMAT

-> 16 - 4√5 + 4√5 -5
->16 – 5
-> 11

so its option C
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Re: (4 + 5^1/2) (4 – 5^1/2) is equal to:?   [#permalink] 15 Dec 2019, 04:06