√2ⁿ = 64
⇒ 2^n/2 = 2⁶

Correct Option: D

√2ⁿ = 64
⇒ 2^n/2 = 2⁶
⇒ n/2 = 6
⇒ n = 12

=√2/3 + 3√3/2
= √2/√3 x √3/√3 + 3√3/√2 x √2/ √2
= √6/3 + 3√6/2
= (2.55 / 3) + [(3 x 2.55) / 2]

Correct Option: D

=√2/3 + 3√3/2
= √2/√3 x √3/√3 + 3√3/√2 x √2/ √2
= √6/3 + 3√6/2
= (2.55 / 3) + [(3 x 2.55) / 2]
= 2.55/3 + 7.65/2
= (5.10 + 22.95)/6
= 28.05/6
= 4.675

1/ (√3 + √2)
= (√3 - √2) / [ 1/ (√3 - √2) x (√3 + √2)]
= (√3 - √2) / (3 - 2)

Correct Option: C

1/ (√3 + √2)
= (√3 - √2) / [ 1/ (√3 - √2) x (√3 + √2)]
= (√3 - √2) / (3 - 2)
= (1.7732 - 1.414) = 0.318

(√32 + √48) / (√8 + √12)
= (√16 x 2 + √16 x 3) / (√4 x 2 + √4 x 3)
= (4√2 + 4√3) / (2√2 + 2√3)
= 4(√2 + √3) / 2(√2 + √3 ) = 2

Correct Option: B

(√32 + √48) / (√8 + √12)
= (√16 x 2 + √16 x 3) / (√4 x 2 + √4 x 3)
= (4√2 + 4√3) / (2√2 + 2√3)
= 4(√2 + √3) / 2(√2 + √3 ) = 2

√176 + √2401
= √176 + 49
= √225 = 15

Correct Option: B

√176 + √2401
= √176 + 49
= √225 = 15