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Which of the following is equivalent to √3+√2?

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Which of the following is equivalent to √3+√2?  [#permalink]

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New post 30 Mar 2017, 01:23
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A
B
C
D
E

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Which of the following is equivalent to √3+√2?

A. \(√5\)
B. \(\sqrt{5+2√6}\)
C. \(\sqrt{6+2√5}\)
D. \(\sqrt{5-2√6}\)
E. \(\sqrt{5+4√6}\)

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Re: Which of the following is equivalent to √3+√2?  [#permalink]

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New post 30 Mar 2017, 01:29
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MathRevolution wrote:
Which of the following is equivalent to √3+√2?

A. \(√5\)
B. \(\sqrt{5+2√6}\)
C. \(\sqrt{6+2√5}\)
D. \(\sqrt{5-2√6}\)
E. \(\sqrt{5+4√6}\)


let x = √3+√2 ------------------I
on squaring both sides,

\(x^2 = (√3+√2)^2\)

\(x^2 = (√3)^2 + (√2)^2 + 2*(√3√2)\)

\(x^2 = 3 + 2 + 2√6\)

\(x^2 = 5 + 2√6\)

taking square root on both sides
x = \(\sqrt{5+2√6}\)
√3+√2 = \(\sqrt{5+2√6}\) (from I)

Hence option B is correct
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Re: Which of the following is equivalent to √3+√2?  [#permalink]

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New post 30 Mar 2017, 10:58
MathRevolution wrote:
Which of the following is equivalent to √3+√2?

A. \(√5\)
B. \(\sqrt{5+2√6}\)
C. \(\sqrt{6+2√5}\)
D. \(\sqrt{5-2√6}\)
E. \(\sqrt{5+4√6}\)


√3+√2=1.73+1.41=3.14

A quick look tells us that only B and C are close.
25^2=625. so sqrt(6) is approx 2.4; hence B=5+4.8=9.8
C=6+2*2.2>10.4

B is closer to our 3.14^2
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Re: Which of the following is equivalent to √3+√2?  [#permalink]

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New post 02 Apr 2017, 17:22
==> You get \(√a+√b=\sqrt{a+b+2√ab}\) because if you square both sides, you get \(a+b+2\sqrt{ab}\) on both sides.
Thus, you get \(√3+√2=\sqrt{5+2√6}\).

The answer is B. Answer: B
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Re: Which of the following is equivalent to √3+√2?  [#permalink]

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New post 01 Mar 2018, 09:54
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Top Contributor
MathRevolution wrote:
Which of the following is equivalent to √3+√2?

A. \(√5\)
B. \(\sqrt{5+2√6}\)
C. \(\sqrt{6+2√5}\)
D. \(\sqrt{5-2√6}\)
E. \(\sqrt{5+4√6}\)


KEY CONCEPT: If we take a positive number, square it and then take the square root of the result, we'll get back to the same number we started with.
For example...
Take: 5
Square it to get: 25
Take the square root: √25
Evaluate: 5

Now let's answer the question:
Take: √3+√2
Square it to get: (√3+√2)(√3+√2)
Use FOIL to expand : 3 + √6 + √6 + 2
Simplify: 5 + 2√6
Take the square root: √(5 + 2√6)

Answer: B

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Re: Which of the following is equivalent to √3+√2? &nbs [#permalink] 01 Mar 2018, 09:54
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