If $$a, b$$ are positive integers such that$$ \sqrt{a}+\sqrt{b}=\sqrt{189}$$, find the value of $$a+b$$

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Uniteasy Admin · Accepted Answer

$$\because \sqrt{189}=3\sqrt{21} $$
Let 
$$x\sqrt{21}+y\sqrt{21}  =3\sqrt{21}$$
$$x+y=3$$
When $$x=1, y=2$$, $$a=21, b=4	imes 21= 84$$
 When $$x=2, y=1$$, $$a=84, b=21$$

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