∴  √64009 = 253

Correct Option: C

∴  √64009 = 253

a = 64 and b = 289
∴  √a = √64 = 8 and
√b = √289 = 17
∴  (√√a + √b − √√b − √a)^1/2
= (√8 + 17 − √17 − 8)^1/2
= (√25 − √9)^1/2
= (5 − 3)^1/2
= (2)^1/2

Correct Option: A

a = 64 and b = 289
∴  √a = √64 = 8 and
√b = √289 = 17
∴  (√√a + √b − √√b − √a)^1/2
= (√8 + 17 − √17 − 8)^1/2
= (√25 − √9)^1/2
= (5 − 3)^1/2
= (2)^1/2

41 × 41 = 1681
42 × 42 = 1764
∴  Required answer
= 1764 – 1728 = 36

Correct Option: A

41 × 41 = 1681
42 × 42 = 1764
∴  Required answer
= 1764 – 1728 = 36

∴  20184 = 2 × 2 × 2 × 3 × 29 × 29 × = 2² × 29² × 2 × 3.
∴  Required number
= 2 × 3 = 6

Correct Option: D

∴  20184 = 2 × 2 × 2 × 3 × 29 × 29 × = 2² × 29² × 2 × 3.
∴  Required number
= 2 × 3 = 6

5808 = 2 × 2 × 2 × 2 × 3 × 11 × 11 = 2² × 2² × 11² × 3
Therefore, when 5808 is multiplied by 3, then it will be perfect square number.

Correct Option: D

5808 = 2 × 2 × 2 × 2 × 3 × 11 × 11 = 2² × 2² × 11² × 3
Therefore, when 5808 is multiplied by 3, then it will be perfect square number.