Simplify 3√8+2√186√2

Mathematics

ScanSolve AI Answer

Answer

626\sqrt{2}

Step-by-step solution

4 steps
  1. Simplify each radical term by finding perfect square factors.

    For 383\sqrt{8}:
    8=4×2=4×2=22\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
    So, 38=3×22=623\sqrt{8} = 3 \times 2\sqrt{2} = 6\sqrt{2}

  2. Simplify the next radical term.

    For 2182\sqrt{18}:
    18=9×2=9×2=32\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
    So, 218=2×32=622\sqrt{18} = 2 \times 3\sqrt{2} = 6\sqrt{2}

  3. Substitute the simplified radicals back into the original expression.

    The expression becomes:

    62+62−626\sqrt{2} + 6\sqrt{2} - 6\sqrt{2}
  4. Combine the like terms.

    (6+6−6)2=62(6+6-6)\sqrt{2} = 6\sqrt{2}

    The final answer is 626\sqrt{2}.

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