In order to solve this problem, we need to use the concept of square root.

Definition of Square Root: The square root of a number is the number which when multiplied by itself, gives the original number.

Formula for Square Root: √x = x1/2

Given Expression : √? = ( 88 x 42) ÷ 16

Step 1 : Let us simplify the expression given

( 88 x 42) ÷ 16

= ( 44 x 42 ) ÷ 8

= ( 22 x 22 x 42) ÷ 8

= ( 22 x 42 x 42 ) ÷ 8

= ( 22 x 1764) ÷ 8

= 39660

Step 2 : Now, let us apply the square root formula

√? = √ ( 39660)

√? = √ ( 39660)1/2

√? = √ ( 39660 x 1/2)

√? = √ ( 19830)

√? = √ ( 19830 x 1/2)

√? = √ ( 9915)

√? = √ ( 9915 x 1/2)

√? = √ ( 4957.5)

√? = √ ( 4957.5 x 1/2)

√? = √ ( 2478.75)

√? = √ ( 2478.75 x 1/2)

√? = √ ( 1239.375)

√? = √ ( 1239.375 x 1/2)

√? = √ ( 619.6875)

√? = √ ( 619.6875 x 1/2)

√? = √ ( 309.84375)

√? = √ ( 309.84375 x 1/2)

√? = √ ( 154.921875)

√? = √ ( 154.921875 x 1/2)

√? = √ ( 77.460938)

√? = √ ( 77.460938 x 1/2)

√? = √ ( 38.730469)

√? = √ ( 38.730469 x 1/2)

√? = √ ( 19.365234)

√? = √ ( 19.365234 x 1/2)

√? = √ ( 9.682617)

√? = √ ( 9.682617 x 1/2)

√? = √ ( 4.8413)

√? = √ ( 4.8413 x 1/2)

√? = √ ( 2.42065)

√? = √ ( 2.42065 x 1/2)

√? = √ ( 1.21032)

√? = √ ( 1.21032 x 1/2)

√? = √ ( 0.60516)

√? = √ ( 0.60516 x 1/2)

√? = √ ( 0.30258)

√? = 0.55132

Hence, the answer is Option D - 53361

If you think the solution is wrong then please provide your own solution below in the comments section .

1. First, we group the digits of the number into pairs, starting from the right: 35, 16, 49.
2. We find the largest perfect square that is less than or equal to 35, which is 25. We subtract 25 from 35 and bring down the next pair of digits to get 116.
3. We double the value of the square root we have found so far (which is 5) and write it as the first digit of the next term of the square root. We then look for the largest digit n such that (20n + n^2) is less than or equal to 116. We find that n = 4, since 20n + n^2 = 80, which is less than 116. We write 4 as the second digit of the next term of the square root.
4. We subtract (20n + n^2) from 116 to get 36, and bring down the last pair of digits (49).
5. We repeat the process by doubling the value of the square root so far (which is 54) and finding the largest digit n such that (20n + n^2) is less than or equal to 3649. We find that n = 3, since 20n + n^2 = 69, which is less than 3649. We write 3 as the third digit of the next term of the square root.
6. We subtract (20n + n^2) from 3649 to get 100, which is a perfect square. We bring down the next pair of zeroes and write them as the last two digits of the square root.