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Distribute sqrt(5) to each term inside the parenthesis.

Mathematics

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Answers

3 parts
a

10+5\sqrt{10} + \sqrt{5}

b

35−103\sqrt{5} - \sqrt{10}

c

16216\sqrt{2}

Step-by-step solution

8 steps

Part a· 2 steps

  1. Distribute 5\sqrt{5} to each term inside the parenthesis.

    5(2+1)=5×2+5×1\sqrt{5}(\sqrt{2} + 1) = \sqrt{5} \times \sqrt{2} + \sqrt{5} \times 1

  2. Multiply the surds and simplify.

    5×2+5=10+5\sqrt{5 \times 2} + \sqrt{5} = \sqrt{10} + \sqrt{5}

    The simplified expression is:

    10+5\boxed{\sqrt{10} + \sqrt{5}}

Part b

35−103\sqrt{5} - \sqrt{10}

  1. Distribute 5\sqrt{5} to each term inside the parenthesis.

    5(3−2)=5×3−5×2\sqrt{5}(3 - \sqrt{2}) = \sqrt{5} \times 3 - \sqrt{5} \times \sqrt{2}

  2. Multiply the terms.

    35−5×2=35−103\sqrt{5} - \sqrt{5 \times 2} = 3\sqrt{5} - \sqrt{10}

    The simplified expression is:

    35−10\boxed{3\sqrt{5} - \sqrt{10}}

Part c

16216\sqrt{2}

  1. Apply the exponent to both factors inside the parenthesis.

    (22)3=23×(2)3(2\sqrt{2})^3 = 2^3 \times (\sqrt{2})^3

  2. Calculate 232^3.

    23=2×2×2=82^3 = 2 \times 2 \times 2 = 8

  3. Calculate (2)3(\sqrt{2})^3.

    (2)3=2×2×2=(2)2×2=2×2=22(\sqrt{2})^3 = \sqrt{2} \times \sqrt{2} \times \sqrt{2} = (\sqrt{2})^2 \times \sqrt{2} = 2 \times \sqrt{2} = 2\sqrt{2}

  4. Multiply the results from Step 2 and Step 3.

    8×22=1628 \times 2\sqrt{2} = 16\sqrt{2}

    The simplified expression is:

    162\boxed{16\sqrt{2}}
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