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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If the sum of the square roots of two integers is [(9+6 2^(1/2)]^(1/2)
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22 Apr 2022, 08:00
22 Apr 2022, 08:00
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Question Stats:
75% (02:09) correct
25% (02:50) wrong based on 4 sessions
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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
(A) 40
(B) 43
(C) 45
(D) 48
(C) 52
Re: If the sum of the square roots of two integers is [(9+6 2^(1/2)]^(1/2)
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23 Apr 2022, 01:06
23 Apr 2022, 01:06
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Solution with explanation
Let x and Y are integers number
So √x+√y= √(9+6√2)
By squiring both side we get,
X+y+2√xy=9+6√2
X+y=9 and 2√xy =6√2 ie xy=18
Using tree method we get, x=3,y=6
x^2+y^2=3^2+6^2=45
Let x and Y are integers number
So √x+√y= √(9+6√2)
By squiring both side we get,
X+y+2√xy=9+6√2
X+y=9 and 2√xy =6√2 ie xy=18
Using tree method we get, x=3,y=6
x^2+y^2=3^2+6^2=45
gmatclubot
Re: If the sum of the square roots of two integers is [(9+6 2^(1/2)]^(1/2) [#permalink]
23 Apr 2022, 01:06
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