If a nine-digit number 389x6378y is divisible by 72, then the value of √(6x + 7y) will be∶

Divisibility law of 8 ⇒ A number divisible by 8 if its last three digits are divisible by 8. Divisibility law of 9 ⇒ A number is divisible by 9 if sum of its digit is divisible by 9. Nine-digit number 389x6378y is divisible by 72, so number also divisible by 8 and 9 also. 78y divisible by 8 if y = 4 so number become 389x63784 Nine-digit number 389x63784 divisible by 9 if sum of its digit divisible by 9. ⇒ 3 + 8 + 9 + x + 6 + 3 + 7 + 8 + 4 ⇒ 48 + x If we put x = 6, the number become 54 which is divisible by 9. So, x = 6 and y = 4 Now, √(6x + 7y) ⇒ √(6 × 6 + 7 × 4) ⇒ √(36 + 28) ⇒ √64 ⇒ 8