When multiplying square roots, multiply the numbers inside the radicals together. This gives sqrt(36), and since 36 is a perfect square, the square root is 6.

Simplify both terms first: sqrt(18) = 3*sqrt(2) and sqrt(8) = 2*sqrt(2). Subtracting them gives 3*sqrt(2) - 2*sqrt(2) = 1*sqrt(2), which is just sqrt(2).

First simplify each radical: sqrt(12) is 2*sqrt(3) and sqrt(27) is 3*sqrt(3). Now that they have the same radicand, add them: 2*sqrt(3) + 3*sqrt(3) = 5*sqrt(3).

The second term has an implicit coefficient of 1. Subtracting 1 from 7 gives 6. The radical part remains the same, producing 6*sqrt(7).

Since the radicands (number under the root) are the same, treat sqrt(5) as a variable. Add the coefficients 2 and 4 to get 6, giving a result of 6*sqrt(5).

Because both terms have sqrt(3), they are like radicals. Simply subtract the coefficients: 5 - 2 = 3, maintaining the radical to get 3*sqrt(3).

You can add radicals just like like terms when the numbers inside the roots are identical. Adding an implicit 1*sqrt(2) to 3*sqrt(2) yields 4*sqrt(2).

Evaluate the numerical and variable parts separately. The square root of 16 is 4, and the square root of x^4 is x^2. This gives the exact simplified form 4x^2.

Rewrite y^5 as the product of the largest perfect square (y^4) and y. The square root of y^4 is y^2, bringing it outside the radical to get y^2*sqrt(y).

Separate x^3 into x^2 * x. Since x^2 is a perfect square, taking its square root gives x on the outside, leaving one x inside the radical: x*sqrt(x).