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# (3^(1/2) + 2)(3^(1/2) - 2) =

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Re: (3^(1/2) + 2)(3^(1/2) - 2) = [#permalink]
Bunuel wrote:
$$(\sqrt{3} + 2)(\sqrt{3} - 2)=$$

A. $$\sqrt{3}-4$$

B. $$\sqrt{6}-4$$

C. -1

D. 1

E. 2

$$(\sqrt{3} + 2)(\sqrt{3} - 2)=$$
= 3-4 =-1

IMO C

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Re: (3^(1/2) + 2)(3^(1/2) - 2) = [#permalink]
Top Contributor
Bunuel wrote:
$$(\sqrt{3} + 2)(\sqrt{3} - 2)=$$

A. $$\sqrt{3}-4$$

B. $$\sqrt{6}-4$$

C. -1

D. 1

E. 2

In case you didn't catch the difference of squares, here's another approach that will still help you reach the correct answer:

------ASIDE------------------------
By test day, all students should have the following approximations memorized:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2
-------------------------------------
When we replace the given values we get:
$$(\sqrt{3} + 2)(\sqrt{3} - 2)≈(1.7 + 2)(1.7 - 2)≈(3.7)(-0.3)≈-1.1$$
So the correct answer must be approximately -1.1

Let's check the answer choices...
A. $$\sqrt{3}-4≈1.7-4≈-2.3$$
No good. Eliminate

B. $$\sqrt{6}-4$$
Since √4 = 2 and √9 = 3, √6 is about 2.4
So, $$\sqrt{6}-4≈2.4-4≈1.6$$
This is pretty close to -1.1, so we'll keep it for now

C. -1
This is closer to -1.1
Keep for now

D. 1
No good. Eliminate

E. 2
No good. Eliminate

So, we are down to answer choices B and C
Since C is closer, we'll take that.

Cheers,
Brent
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Re: (3^(1/2) + 2)(3^(1/2) - 2) = [#permalink]
The answer is C
It is a simple question which uses the formula a+b)(a-b) equals a2+b2
By using this formula we can get the answer

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Re: (3^(1/2) + 2)(3^(1/2) - 2) = [#permalink]
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Re: (3^(1/2) + 2)(3^(1/2) - 2) = [#permalink]
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