Simplify the square root of 3 times the fifth root of 3. three to the one tenth power three to the three fifths power

Question

Simplify the square root of 3 times the fifth root of 3.

three to the one tenth power
three to the three fifths power
three to the nine tenths power
three to the seven tenths power

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Cora 18 mins 2021-10-14T03:55:54+00:00 2 Answers 0

Answers ( )

    0
    2021-10-14T03:56:57+00:00

    Answer:

    The last option:  3^(7/10).

    Step-by-step explanation:

    √3 *  ⁵√3

    = 3^1/2 * 3*1/5

    = 3^(1/2*1/5)

    = 3^(7/10).

    0
    2021-10-14T03:57:20+00:00

    Answer:

    Three to the three fifths power.

    Step-by-step explanation:

    The given expression is

    \sqrt{3\sqrt[5]{3} }

    To simplify this expression, we have to use a specific power property which allow us to transform a root into a power with a fractional exponent, the property states:

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

    Applying the property, we have:

    \sqrt{3\sqrt[5]{3}}=\sqrt{3(3)^{\frac{1}{5}}}=(3(3)^{\frac{1}{5}})^{\frac{1}{2}}

    Now, we multiply exponents:

    (3(3)^{\frac{1}{5}})^{\frac{1}{2}}\\3^{\frac{1}{2}}3^{\frac{1}{10}}

    Then, we sum exponents to get the simplest form:

    3^{\frac{1}{2}}3^{\frac{1}{10}}=3^{\frac{1}{2}+\frac{1}{10}} =3^{\frac{10+2}{20}}=3^{\frac{12}{20}}  \\\therefore \sqrt{3\sqrt[5]{3}}=3^{\frac{3}{5} }

    Therefore, the right answer is three to the three fifths power.

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