What is the simplified form of the following expression? 5sqrt 8-sqrt18-2sqrt2

Question

What is the simplified form of the following expression? 5sqrt 8-sqrt18-2sqrt2

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Everleigh 2 weeks 2021-09-09T13:50:45+00:00 2 Answers 0

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    0
    2021-09-09T13:52:24+00:00

    Answer:

    5 sqrt2.

    Step-by-step explanation:

    sqrt8 = sqrt4 * sqrt2 = 2 sqrt2

    sqrt18 = sqrt9 * sqrt2 = 3 sqrt2

    So simplifying:

    5sqrt 8 – sqrt18 – 2 sqrt2

    = 5*2sqrt2 – 3 sqrt 2 – 2 sqrt2

    = 10 sqrt2 – 5 sqrt2

    = 5 sqrt2 (answer).

    0
    2021-09-09T13:52:39+00:00

    For this case we must simplify the following expression:

    5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}

    Rewriting we have:

    8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =

    We have that by definition of properties of roots and powers it is fulfilled:

    \sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

    So:

    5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}

    Answer:

    5 \sqrt {2}

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