Square root 18 + 3/square root 2

To simplify the expression square root 18 + 3/square root 2, we can start by simplifying each term.

First, let's simplify the square root of 18:
The square root of 18 can be written as the square root of 9 times 2, because 9 is a perfect square: sqrt(9) x sqrt(2) = 3 sqrt(2).

Next, let's simplify the fraction 3/square root 2:
To eliminate the square root in the denominator, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of square root 2 is -sqrt(2), so multiply the fraction by -sqrt(2)/-sqrt(2):
(3/sqrt(2)) x (-sqrt(2)/-sqrt(2)) = -3sqrt(2)/2

Now, let's substitute these simplified terms back into the original expression:
3 sqrt(2) + (-3sqrt(2)/2)

Since both terms have the same square root (sqrt(2)), we can simply combine the coefficients:
3 sqrt(2) - (3sqrt(2)/2)

To simplify, we need to find a common denominator for the two terms. Since the first term doesn't have a denominator, we can rewrite it as (3 sqrt(2) x 2/2):
(3 sqrt(2) x 2)/2 - (3sqrt(2)/2)

Simplifying further:
(6 sqrt(2))/2 - (3sqrt(2)/2)

Combine the terms:
(6 sqrt(2) - 3sqrt(2))/2

Finally, we can subtract the square root terms since they have the same radical:
(6 - 3) sqrt(2)/2

The final simplified expression is:
3 sqrt(2)/2