Question

Using the digits 1 to 9, at most one time each, fill in the boxes to make the

following expression as close to O as possible.
1
V
OTVO

Answer 1

By assigning the smallest available digits to the variables, the expression
`\(√(abc) - √(de) - √(f)\)` which can be written as
`\(√(123) - √(45) - √(6)\)` is minimized to approximately 1.93.

To minimize the expression
`\(√(abc) - √(de) - √(f)\)`, where each letter represents a distinct digit from 1 to 9, our goal is to assign values to (a), (b), (c), (d), (e), and (f) that result in the smallest possible values for each term.

Considering the nature of square roots, we aim to minimize each digit by selecting the smallest available ones. A suitable assignment is a = 1, b = 2, c = 3, d = 4, e = 5, and f = 6. This choice prioritizes the smaller digits for each variable.

The expression now becomes
`\(√(123) - √(45) - √(6)\)`. Evaluating each square root, we get
`\(√(123) \approx 11.09\)`,
`\(√(45) \approx 6.71\)`, and
`\(√(6) \approx 2.45\)`.

Therefore, the minimized expression is 11.09 - 6.71 - 2.45
`\approx 1.93\)` , bringing it as close to 0 as possible.

Answer 2

Explanation:

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