SOLUTION: Add 8(the square root of)20 + 6(the square root of)125. Simplify by collecting like radical terms if possible.

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Question 401439: Add 8(the square root of)20 + 6(the square root of)125. Simplify by collecting like radical terms if possible.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
8%2Asqrt%2820%29%2B6%2Asqrt%28125%29
Like radical terms are terms where the radical(s) all have the same index and radicand. ("radicand" is the expression inside a radical.) All of your terms are square roots (whose implied index is 2) so the indices are the same. But the radicands, 20 and 125, are different! So these terms are not like radical terms...yet.

Both of these square roots have perfect square factors so they can be simplified:
8%2Asqrt%284%2A5%29%2B6%2Asqrt%2825%2A5%29
8%2Asqrt%284%29%2Asqrt%285%29%2B6%2Asqrt%2825%29%2Asqrt%285%29
8%2A2%2Asqrt%285%29%2B6%2A5%2Asqrt%285%29
16%2Asqrt%285%29%2B30%2Asqrt%285%29
Now that they have been simplified we can see that they are now like radical terms. (This is one of the reasons we always simplify radicals when possible.) So we can now add them.

To add or subtract like radical terms you just add or subtract the coefficients. It is just like adding/subtracting variable terms! So adding/subtracting
16%2Asqrt%285%29%2B30%2Asqrt%285%29
is just like adding
16x + 30x
So just like
16x + 30x = 46x
16%2Asqrt%285%29%2B30%2Asqrt%285%29+=+46sqrt%285%29

Note 1: When adding/subtracting radical terms, nothing changes with the radicals. Only the coefficient get added/subtracted.
Note 2: Not all radical terms can be added. Only like radical terms can be added (or subtracted). After we simplified the original square roots, they may not have turned out to be like terms.