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Evaluate 2 sqrt(8) + 3 sqrt(3)

Mathematics

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Answer

2\textbf{2}

Step-by-step solution

4 steps

Here's the solution for 1(a)i:

  1. Rewrite the terms inside the logarithms using powers.

    8=81/2=(23)1/2=23/2\sqrt{8} = 8^{1/2} = (2^3)^{1/2} = 2^{3/2} 3=31/2\sqrt{3} = 3^{1/2}

  2. Substitute these exponential forms back into the expression.

    log⁡2(23/2)+log⁡3(31/2)\log_2 (2^{3/2}) + \log_3 (3^{1/2})

  3. Apply the logarithm property log⁡b(bx)=x\log_b (b^x) = x.

    32+12\frac{3}{2} + \frac{1}{2}

  4. Add the fractions.

    32+12=3+12=42=2\frac{3}{2} + \frac{1}{2} = \frac{3+1}{2} = \frac{4}{2} = 2

    The value of the expression is 2\textbf{2}.

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