SOLUTION: Square root of 8 plus 3 times the square root of 8 minus 3

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Question 817827: Square root of 8 plus 3 times the square root of 8 minus 3
Found 2 solutions by FightinBlueHens, jsmallt9:
Answer by FightinBlueHens(27) About Me  (Show Source):
You can put this solution on YOUR website!
√8 + 3√8 - 3 = 4 √8 – 3

√8 = √(4*2) = 2 √2
4 √8 – 3 = 4*2 √2 - 3
= 8√2 - 3

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%288%29%2B3sqrt%288%29-3
The two square root terms are like terms. (Like radical terms are the same type of root and have the same radicands. ("Radicand" is the name for the expression inside a radical.) Our radicals are both square roots with radicands of 8 so we can add them together. Exactly like x + 3x = 4x, sqrt%288%29%2B3sqrt%288%29+=+4sqrt%288%29. After adding our expression is:
4%2Asqrt%288%29-3

All that is left is to simplify the square root. 8 has a perfect square factor, 4, so it will simplify:
4%2Asqrt%284%2A2%29-3
4%2Asqrt%284%29%2Asqrt%282%29-3
4%2A2%2Asqrt%282%29-3
which simplifies to:
8%2Asqrt%282%29-3