SOLUTION: Simplify: 5√20+2√18-√50+2√125

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Question 613323: Simplify:
5√20+2√18-√50+2√125
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
5sqrt%2820%29%2B2sqrt%2818%29-sqrt%2850%29%2B2sqrt%28125%29
None of these terms are like terms with each other so we cannot add them as they are. (Like square root terms have the same radicands. ("Radicand" is the name for the expression inside a radical.) But each of the square roots has a perfect square factor in its radicand. So each of the square roots will simplify:
5sqrt%284%2A5%29%2B2sqrt%289%2A2%29-sqrt%2825%2A2%29%2B2sqrt%2825%2A5%29

5%2A2%2Asqrt%285%29%2B2%2A3%2Asqrt%282%29-5%2Asqrt%282%29%2B2%2A5%2Asqrt%285%29
10%2Asqrt%285%29%2B6%2Asqrt%282%29-5%2Asqrt%282%29%2B10%2Asqrt%285%29

With the square roots simplified, we can now see some like terms. The first and last terms are like terms. And the 2nd and 3rd terms are like terms. And, exactly like 10x + 10x = 20x, 10sqrt%285%29%2B10sqrt%285%29+=+20sqrt%285%29. And exactly like 6x-5x = x, 6sqrt%282%29-5sqrt%282%29+=+sqrt%282%29. So our expression simplifies to:
20sqrt%285%29+%2B+sqrt%282%29