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Which of these equations is correct? sqrt(16)+sqrt(9)=sqrt(16+9) sqrt(16)+sqrt(12)=sqrt(16+12) Neither is incorrect. b. Both are incorrect.

Mathematics

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Answer

d. Both are incorrect.\text{d. Both are incorrect.}

Step-by-step solution

3 steps

Here's how to determine which equations are incorrect:

  1. Evaluate the first equation

    16+3=16+3\sqrt{16} + \sqrt{3} = \sqrt{16+3}.
    Calculate the left side (LS):

    16+3=4+3\sqrt{16} + \sqrt{3} = 4 + \sqrt{3}

    Calculate the right side (RS):

    16+3=19\sqrt{16+3} = \sqrt{19}

    Since 4+3≠194 + \sqrt{3} \neq \sqrt{19}, the first equation is incorrect.

  2. Evaluate the second equation

    6+12=6+12\sqrt{6} + \sqrt{12} = \sqrt{6+12}.
    Calculate the left side (LS):

    6+12=6+4×3=6+23\sqrt{6} + \sqrt{12} = \sqrt{6} + \sqrt{4 \times 3} = \sqrt{6} + 2\sqrt{3}

    Calculate the right side (RS):

    6+12=18=9×2=32\sqrt{6+12} = \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}

    Since 6+23≠32\sqrt{6} + 2\sqrt{3} \neq 3\sqrt{2}, the second equation is incorrect.

  3. Determine the correct option based on the evaluations.

    Both equations are incorrect.

    The final answer is d. Both are incorrect.\text{d. Both are incorrect.}.

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