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Question

If √[18-6√5] =√a-√b, then prove a + b= 18

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Solution

√a-√b=√(18-6√5)
Squaring both sides,
(√a-√b)²={√(18-6√5)}²
or, a+b-2√a√b=18-6√5
or, (a+b)-2√a√b=(15+3)-2.√15.√3
Comparing both sides we get,
a+b=15+3=18 (Proved)

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