1st digit is square root of 2nd digit

2nd digit is square of 1st sum of 3rd & 6th is 14 sum of 3rd 4th 5th & 6th is square of 4th sum of all digit is 37 multiplication of 1st & 5th is sum of 4th 5th & 6th sum of 2nd 3rd & 4th is multiplication of 1st & last.now

assuming six digits, a,b,c,d,e,f, we have

a = √b
b = a^2 (well, duh)
c+f = 14
c+d+e+f = d^2
a+b+c+d+e+f = 37
ae = d+e+f
b+c+d = af

Play around with that for a while.

To solve this problem, we need to analyze the given information and derive the digits of the number.

Let's break down the given information:

1. The 1st digit is the square root of the 2nd digit: Let's represent the 1st digit as 'A' and the 2nd digit as 'B'. From this statement, we have the equation sqrt(B) = A.

2. The 2nd digit is the square of the sum of the 1st digit and the 6th digit: Let's represent the 6th digit as 'F'. We have the equation (A + F)^2 = B.

3. The sum of the 3rd and 6th digits is 14: Let's represent the 3rd digit as 'C'. We have the equation C + F = 14.

4. The sum of the 3rd, 4th, 5th, and 6th digits is the square of the 4th digit: Let's represent the 4th digit as 'D'. We have the equation C + D + E + F = D^2.

5. The sum of all the digits is 37: We can represent the sum as A + B + C + D + E + F = 37.

6. The multiplication of the 1st and 5th digit is the sum of the 4th, 5th, and 6th digits: Let's represent the 5th digit as 'E'. We have the equation A * E = D + E + F.

7. The sum of the 2nd, 3rd, and 4th digits is the multiplication of the 1st and last digit: Let's represent the last digit as 'G'. We have the equation B + C + D = A * G.

Now, let's solve these equations step by step to find the values of each digit.

From equation 3, we get C + F = 14, which means F = 14 - C.

Substituting the value of F in equation 2, we have (A + 14 - C)^2 = B.

Using equation 6, we get A * E = D + E + (14 - C).

Since we know the sum of all the digits is 37 (equation 5), we can write A + B + C + D + E + F = 37 as:
A + B + C + D + E + (14 - C) = 37,
A + B + D + E = 23. (equation 8)

Using equation 4, we have C + D + E + (14 - C) = D^2, which simplifies to:
D^2 - D - E + 14 = 0. (equation 9)

From equation 7, we have B + C + D = A * G, which can be rewritten as D = A * G - (B + C). (equation 10)

Now, let's solve these equations together to find the values of the digits.

Start by solving equations 9 and 10 simultaneously. We have:
D^2 - D - E + 14 = 0,
D = A * G - (B + C).

Substitute the value of D in equation 9, we get:
(A * G - (B + C))^2 - (A * G - (B + C)) - E + 14 = 0.

Expand and simplify this equation to get the quadratic equation:
(A^2 * G^2) - (2 * A * G * (B + C)) + ((B + C)^2) - (A * G) + (B + C) - E + 14 = 0.

Now, we have a system of equations:
(A + 14 - C)^2 = B, (equation 11)
A * E = (A * G - (B + C)) + E + 14, (equation 12)
(A^2 * G^2) - (2 * A * G * (B + C)) + ((B + C)^2) - (A * G) + (B + C) - E + 14 = 0. (equation 13)

With three equations (equations 11, 12, and 13) and three unknowns (A, B, C), we can solve for their values using various algebraic methods such as substitution or elimination.