SOLUTION: Add. Simplify by collecting like radical terms, if possible. sqroot80 + sqroot20

Question 242568: Add. Simplify by collecting like radical terms, if possible.
sqroot80 + sqroot20
Answer by College Student(505) (Show Source): You can put this solution on YOUR website!
First, let's take a look at 20. What two numbers multiply with each other to equal 20? We have 20x1, 10x2, and 4x5.
* We'll forget 20x1 because it will not get us anywhere.
* How about 10x2. Could we take the square root of either number and come up with an integer? No.
* How about 4x5. Could we take the square root of either number and come up with an integer? Yes. The square root of 4 is 2.
*** So we can say that = = ... which takes us to right?
.
Let's work with 80. What two numbers multiply with each other to equal 80? We have 80x1, 40x2, 20x4, 16x5, 80/8.
* We'll forget 80x1 because it will not get us anywhere.
* How about 20x4. Could we take the square root of either number and come up with an integer? Yes, square root of 4 is 2, but we'll end up with sqrt 20... and we'd have to repeat the steps for the square root of 20.
* How about 16x5. Could we take the square root of either number and come up with an integer? Yes. The square root of 16 is 4 and we're left with square root of 5. Let's take this one because we will then end up with the same square root as before AND this will allow us to add the results.
*** So we can now say that = = ... which takes us to right?
.
We can now simplify the expression
from:
to:
to: <--- our final answer!
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