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

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by M7MBA » Thu Mar 01, 2018 6:47 am
Which of the following is equivalent to √3+√2? $$\left(A\right)\ \sqrt{5}$$ $$\left(B\right)\ \sqrt{5+2\sqrt{6}}$$ $$\left(C\right)\ \sqrt{6+2\sqrt{5}}$$ $$\left(D\right)\ \sqrt{5-2\sqrt{6}}$$ $$\left(E\right)\ \sqrt{5+4\sqrt{6}}$$ The Oa is the option B.

Experts, how can I rewrite the given expression to get one of the listed options? Can you show me the calculation needed? <i class="em em-confused"></i>
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by Brent@GMATPrepNow » Thu Mar 01, 2018 9:51 am
M7MBA wrote:Which of the following is equivalent to √3+√2? $$\left(A\right)\ \sqrt{5}$$ $$\left(B\right)\ \sqrt{5+2\sqrt{6}}$$ $$\left(C\right)\ \sqrt{6+2\sqrt{5}}$$ $$\left(D\right)\ \sqrt{5-2\sqrt{6}}$$ $$\left(E\right)\ \sqrt{5+4\sqrt{6}}$$
Nice question!

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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by BTGmoderatorRO » Fri Mar 02, 2018 11:55 am
$$Take\ the\ square\ of\ \ \left(\sqrt{3}+\sqrt{2}\right)^2$$
$$\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)=3+\sqrt{6}+\sqrt{6}+2$$
$$5+2\sqrt{6}$$
$$Take\ the\ square\ root\ of\ our\ result$$
$$we\ have\ \sqrt{5+2\sqrt{6}}$$
This correspond with option b
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by Scott@TargetTestPrep » Mon Jul 01, 2019 4:13 pm
M7MBA wrote:Which of the following is equivalent to √3+√2? $$\left(A\right)\ \sqrt{5}$$ $$\left(B\right)\ \sqrt{5+2\sqrt{6}}$$ $$\left(C\right)\ \sqrt{6+2\sqrt{5}}$$ $$\left(D\right)\ \sqrt{5-2\sqrt{6}}$$ $$\left(E\right)\ \sqrt{5+4\sqrt{6}}$$ The Oa is the option B.

Experts, how can I rewrite the given expression to get one of the listed options? Can you show me the calculation needed? <i class="em em-confused"></i>
We see that the given choices are all in square roots. So if we square (√3 + √2), it should give us the radicand in one of the given choices.

(√3 + √2)^2 = (√3)^2 + (√2)^2 + 2(√3)(√2) = 3 + 2 + 2√6 = 5 + 2√6

Since (√3 + √2)^2 = 5 + 2√6, then √(5 + 2√6) = √3 + √2.

Answer: B

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