Can someone help me with this? I don’t understand? \sqrt[3]{1000 {}^{2} } How do you do the whole process? I need som

Question

Can someone help me with this? I don’t understand?
\sqrt[3]{1000 {}^{2} }
How do you do the whole process? I need some explanation…
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Khang Minh 5 years 2021-08-26T03:22:19+00:00 2 Answers 18 views 0

Answers ( )

  1. giabao
    0
    2021-08-26T03:23:30+00:00
    Reply

    9514 1404 393

    Answer:

      100

    Step-by-step explanation:

    A root is equivalent to a fractional power. A square root is a 1/2 power. A cube root is a 1/3 power. The index of the root is the denominator of the fraction.

    Of course the usual rules of exponents apply in evaluating an expression.

      (a^b)^c = a^(bc)

    __

    Your expression can be simplified as follows.

      \displaystyle\sqrt[3]{1000^2}=(1000^2)^{\frac{1}{3}}=1000^{\frac{2}{3}}=(10^3)^{\frac{2}{3}}=10^2=\boxed{100}

    It can also be simplified another way:

      \displaystyle\sqrt[3]{1000^2}=\sqrt[3]{(10^3)^2}=\sqrt[3]{(10^2)^3}=10^2=100

    _____

    Additional comments

    A problem like this is simpler if you are familiar with the squares and cubes of small integers.

  2. binhan
    0
    2021-08-26T03:24:02+00:00
    Reply

    Factor out the 2 so it’s radical 1000. Answer is 100

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