To solve the equation, we can first factor the numbers under the square roots.

When a factor appears twice, we can take it out of the square root.

Now the numbers can be added directly because the expressions under the square roots match.

First, we can simplify the radicals by factoring.

Now, we can factor out the.

Now divide and simplify.

To begin with, factor out the contents of the radicals. This will make answering much easier:

They both have a common factor. This means that you could rewrite your equation like this:

This is the same as:

These have a common. Therefore, factor that out:

These three roots all have ain common; therefore, you can rewrite them:

Now, this could be rewritten:

Now, note that

Therefore, you can simplify again:

Now, that looks messy! Still, if you look carefully, you see that all of your factors have; therefore, factor that out:

This is the same as:

Begin by factoring out the relevant squared data:

is the same as

This can be simplified to:

Since your various factors contain square roots of, you can simplify:

Technically, you can factor out a:

Begin by breaking apart the square roots on the left side of the equation:

This can be rewritten:

You can combine like terms on the left side:

Solve by dividing both sides by:

This simplifies to:

To begin solving this problem, find the greatest common perfect square for all quantities under a radical.

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Pullout of each term on the left:

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Next, factor outfrom the left-hand side:

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Lastly, isolate:

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Solving this one is tricky. At first glance, we have no common perfect square to work with. But since each term can produce the quantity, let's start there:

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Simplify the first term:

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Divide all terms byto simplify,

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Next, factor outfrom the left-hand side:

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Isolateby dividing byand simplifying:

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Last, simplify the denominator:

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Right away, we notice thatis a prime radical, so no simplification is possible. Note, however, that both other radicals are divisible by.

Our first step then becomes simplifying the equation by dividing everything by:

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Next, factor outfrom the left-hand side:

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Lastly, isolate:

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Once again, there are no common perfect squares under the radical, but with some simplification, the equation can still be solved for:

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Simplify:

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Factor outfrom the left-hand side:

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Lastly, isolate:

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