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

#### Question

#### 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\times 21= 84

When x=2, y=1, a=84, b=21

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

\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\times 21= 84

When x=2, y=1, a=84, b=21