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

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Re: Which of the following is equivalent to √3+√2? [#permalink]
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==> 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 $$√3+√2=\sqrt{5+2√6}$$.

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Which of the following is equivalent to √3+√2? [#permalink]
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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. $$\sqrt{5+4√6}$$

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

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)

Originally posted by BrentGMATPrepNow on 01 Mar 2018, 10:54.
Last edited by BrentGMATPrepNow on 25 May 2020, 12:53, edited 1 time in total.
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Re: Which of the following is equivalent to √3+√2? [#permalink]
GMATPrepNow wrote:
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

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)

RELATED VIDEO

why the logic is not to square each number individually rather than collectively ? so, taking √3+√2, then squaring them individually will equal 3+2 = 5. then square root this to come with √5 , A.
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Which of the following is equivalent to 3+2? [#permalink]
Which of the following is equivalent to √3+√2?

Let √x = √3+√2
Squaring both sides,
=> x = 3 + 2 +2√6
=> x = 5+2√6

therefore, √x = √3+√2 = √(5+2√6)

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