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# If the sum of the square roots of two integers is

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Senior Manager
Joined: 29 Jun 2017
Posts: 431
Re: If the sum of the square roots of two integers is  [#permalink]

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24 Oct 2018, 23:48
how do we know that
x+y=9
and
2 square root of xy= 6 square root of 2
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8574
Location: Pune, India
Re: If the sum of the square roots of two integers is  [#permalink]

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25 Oct 2018, 00:08
Bunuel wrote:
If the sum of the square roots of two integers is $$\sqrt{9+6\sqrt{2}}$$, what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52

Let the two integers be a and b.

$$\sqrt{a} + \sqrt{b} = \sqrt{9+6\sqrt{2}}$$

Squaring both sides, we get

$$a + b + 2\sqrt{ab} = 9 + 6\sqrt{2}$$

Since a and b are integers, so $$2\sqrt{ab} = 6\sqrt{2}$$

$$\sqrt{ab} = 3*\sqrt{2} = \sqrt{3*3*2}$$

So values of a and b such that ab = 3*3*2 and sum is 9 is 6 and 3.

$$a^2 + b^2 = 6^2 + 3^2 = 45$$

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Re: If the sum of the square roots of two integers is &nbs [#permalink] 25 Oct 2018, 00:08

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