Question : The value of (√32 + √48) / (√8 + √12) is equal to
(a) √2
(b) 2
(c) 4
(d) 8
Doubt by Suraj
Solution :
(√32 + √48) / (√8 + √12)
=(√48 + √32) / (√12 + √8)
=(4√3 + 4√2) / (2√3 + 2√2)
Rationalising the denominator
=(4√3 + 4√2) × (2√3 - 2√2) / (2√3 + 2√2)×(2√3 - 2√2)
=[4√3(2√3 - 2√2) + 4√2(2√3 - 2√2)] / [(2√3)² - (2√2)²]
[∵(a+b)(a-b)=(a²-b²)]
=[8×3-8√6+8√6-8×2] / [12-8]
=[24-0-16] / 4
=[8]/4
=2
Hence, (b) 2, would be the correct option.