**Solution:**

To evaluate the expression **√5 √2 / √5 - √2**, we can simplify it step by step.

Let's begin by simplifying the expression √5 √2.

**Simplifying √5 √2:**

We can simplify the expression √5 √2 by multiplying the square roots together.

√5 √2 = √(5 * 2) = √10

Given that √10 = 3.162, we can substitute this value back into the original expression:

**Substituting √10 = 3.162:**

√5 √2 / √5 - √2 = √10 / √5 - √2

= 3.162 / √5 - √2

Now we need to rationalize the denominator, which means getting rid of any square roots in the denominator.

**Rationalizing the Denominator:**

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator.

The conjugate of √5 - √2 is √5 + √2.

Multiplying the numerator and denominator by the conjugate:

(3.162 / √5 - √2) * (√5 + √2) / (√5 + √2)

= (3.162 * (√5 + √2)) / ((√5 - √2) * (√5 + √2))

Using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)) in the denominator:

= (3.162 * (√5 + √2)) / (5 - 2)

= (3.162 * (√5 + √2)) / 3

= (√5 + √2) * 3.162 / 3

Simplifying further:

= (√5 * 3.162 + √2 * 3.162) / 3

= (3.162√5 + 3.162√2) / 3

= 1.054√5 + 1.054√2

So, the evaluated value of the expression √5 √2 / √5 - √2, given that √10 = 3.162, is 1.054√5 + 1.054√2.

1.45430995