If $\sqrt{a}+\sqrt{b}=5\sqrt2,$ and $a\cdot b=144,$ what is the value of $a+b?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun Nov 29, 2020 12:45 am

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If $\sqrt{a}+\sqrt{b}=5\sqrt2,$ and $a\cdot b=144,$ what is the value of $a+b?$

A. $\sqrt{26}$
B. $\sqrt{38}$
C. $\sqrt{338}$
D. $26$
E. $38$

Answer: D

Source: EMPOWERgmat

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Source: Beat The GMAT — Problem Solving | Sun Nov 29, 2020 12:45 am

mathisfun: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Nov 29, 2020 10:52 am

Re: If $\sqrt{a}+\sqrt{b}=5\sqrt2,$ and $a\cdot b=144,$ what is the value of $a+b?$

by mathisfun » Sun Nov 29, 2020 11:01 am

Squaring both sides,
a + b + 2root (ab)= 50
a + b + 2 root(144)= 50
a+b= 50-24 = 26

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