2 √10 - 5√3
2 √5 - 5√6
5 √10 - 2√3
3 √5 - 8√6
Correct answer is B
√170−20√30=√a−√b
Squaring both sides,
170−20√30=a+b−2√ab
Equating the rational and irrational parts, we have
a+b=170...(1)
2√ab=20√30
2√ab=2√30×100=2√3000
ab=3000...(2)
From (2), b=3000a
a+3000a=170⟹a2+3000=170a
a2−170a+3000=0
a2−20a−150a+3000=0
a(a−20)−150(a−20)=0
a = 20 or a = 150
∴
\sqrt{170 - 20\sqrt{30}} = \sqrt{20} - \sqrt{150} or \sqrt{150} - \sqrt{20}
= 2\sqrt{5} - 5\sqrt{6} or 5\sqrt{6} - 2\sqrt{5}
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