The expression 
is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 5 (3+ 2√2)
Concept
Rationalization
Application
[15(√10 + √5)] ÷ [(√10 + √20 + √40 - √5 - √80)]
[15 × √5(√2 + √1)] ÷ [√ 5 × (√2 + √4 + √8 - 1 - √16)]
[15 × (√2 + √1)] ÷ [ (√2 + 2 + √8 - 1 - 4)]
[15 × (√2 + √1)] ÷ [√2(1 + 2) - 3]
[15 × (√2 + √1)] ÷ [3√2 - 3]
[15 × (√2 + √1)] ÷ [3(√2 – 1)]
[5 × (√2 + √1)] ÷ [(√2 – 1)]
By rationalizing
[5(√2 + √1)] / [(√2 – 1)] × [(√2 + 1) / (√2 + 1)]
[5(√2 + √1)2] / [(√2 – 1)(√2 + 1)]
[5(2 + 1 + 2√2)]
[5(3 + 2√2)]