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Simplify sqrt(18).

Mathematics

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Answer

24

Step-by-step solution

3 steps

To solve the expression 18×32\sqrt{18} \times \sqrt{32}, we can simplify each square root first.

  1. Simplify 18\sqrt{18}.

    We find the largest perfect square factor of 18.
    18=9×218 = 9 \times 2
    So, 18=9×2=9×2=32\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}.

  2. Simplify 32\sqrt{32}.

    We find the largest perfect square factor of 32.
    32=16×232 = 16 \times 2
    So, 32=16×2=16×2=42\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}.

  3. Multiply the simplified square roots.

    18×32=(32)×(42)\sqrt{18} \times \sqrt{32} = (3\sqrt{2}) \times (4\sqrt{2})

    Multiply the coefficients and the square roots separately:

    =(3×4)×(2×2)=12×(2)2=12×2=24= (3 \times 4) \times (\sqrt{2} \times \sqrt{2}) \\ = 12 \times (\sqrt{2})^2 \\ = 12 \times 2 \\ = 24

    Alternatively, we can multiply the numbers inside the square root first:

    18×32=18×32=576\sqrt{18} \times \sqrt{32} = \sqrt{18 \times 32} \\ = \sqrt{576}

    Now, find the square root of 576.

    576=24\sqrt{576} = 24

    The final answer is 24.

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