Rewrite the first term using a factor of a perfect square.

Combine like-terms.

The answer is:  

Break up the radical that can be simplified.

Rewrite the expression.

A radical multiplied by itself will eliminate the radical and leave just the integer.

The answer is:  

Evaluate by rewriting both radicals by factors of perfect squares.

The radicals  and  cannot be factored anymore, which means we will need to multiply them and combine as one radical.

Simplify this radical.

Replace the term.

The answer is:   

Simplify each radical using values of perfect squares as factors.

Replace the terms into the original expression and simplify.

The answer is:  

Multiply all the terms in the radical to combine as one radical.

Rewrite the radical using known perfect squares as factors.

Simplify the known radicals.

The answer is:  

The best way to approach this problem is to try to pull out perfect squares. In this case the x squared term can be separated from the 80. The 80 can then be broken down into 16, a perfect square, and 5.

Simplify the x squared and root 16 terms.

The goal of simplifying a radical by factoring is to find a factor of the radicand that has a neat whole number as a square root. If this factor is difficult to determine simply by looking at the radicand, a good way to start is by factoring the radicand until you notice a factor that has a whole number as a square root, and can therefore be taken out of the radical. Assuming we couldn't identify a factor of 150 with a neat square root, we could start the factoring by taking out the smallest factor possible, which for even numbers would be 2:

Neither number has a neat square root, so we'll continue by factoring out the next smallest factor of 3 from 75:

At this point we can see that one of our factors, 25, has a neat square root of 5, which we can take out from under the radical, and now that none of the factors left under the radical can be simplified any further, we simply multiply them back together to give us the most simplified form of our radical:

To simplify this expression, I'd recommend factoring it down to its prime factors: . Then for every trio of the same term, place one out of the radical and cross out the trio. Therefore, outside of the radical, you should have and you should have leftover. Then, combine those to get: .

Find the lease common denominator: 

A radical cannot be in the denominator:

To solve this equation, we have to factor our radicals.  We do this by finding numbers that multiply to give us the number within the radical. 

Add them together:

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them: