Question

If the eight-digit number 342x8y6 is divisible by 72, then what is the value of √9x+y, for the largest value of y?​

Answer 1

Answer:

The std form of 36 by - 24 is

Answer 2

The value of √(9x + y) = 3√5

Step-by-step explanation:

Given details:

The Eight digit number = 342x8y6

y should have maximum value from its required values to be divisible by 72.  

                                                                                          (detail 1)

It is divisible by 72,

To find:

the value of $\sqrt{9x + y}$

$72 =( 2\times 2\times 2)\times (3\times 3) =8 \times 9$

It means

To be divisible by 72,  the number has to be divisible by  8 as well as 9.

So,

342x8y6 is divisible by 9 when sum of all the digits of number is divisible by 9.

So,     (3+4+2+x+8+y+6) = 23 + x + y = 9n                   (equation 1)

Similarly 342x8y6 is divisible by 8 when the last three digits of number is divisible by 8.

So,   8y6 is divisible by 8 when y = 1 or 9

It means last three digits are       816   or  896        

So  y = 9                       (because of detail 1)            (equation 2)

Putting equation 2 into equation 1 .

23 + x + 9  should be divisible by 9

= 32 + x should be divisible by 9

So, 32 + x = 36  

So,   x = 4

So, The value of x = 4 and y = 9

and the number =   3424896

$\textbf{\Large So, the value of } \sqrt{9x + y} = \sqrt{(9\times 4) + 9}\\\\ = \sqrt{45} = \sqrt{9\times 5} = 3\sqrt{5}$