If a nine-digit number 389 x 6378 y is divisible by 72, then the value of $$\sqrt{6x + 7y}$$ will be:

389x6378y is divisible by 72,

Factor of 72 = 8 $$\times$$ 9

So, number is divisible by 8 and 9 both.

Divisibility rule for 8,

78y (last three digits should be divisible by 8)

784 is divisible by 8 so, 
Value of y = 4

Divisibility rule of 9,

3 + 8 + 9 + x + 6 + 3 + 7+ 8 + 4

= 48 + x

54 is divisible by 9

So, x = 54 - 48 = 6
Value of $$\sqrt{6x + 7y}$$
= $$\sqrt{6 \times 6 + 7 \times 4}$$
= $$\sqrt{36 + 28}$$ =$$\sqrt{64}$$
= 8