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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Answer 1

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

Answer 2

9514 1404 393

Answer:

100

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)

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Your expression can be simplified as follows.

`\displaystyle\sqrt[3]{1000^2}=(1000^2)^{(1)/(3)}=1000^{(2)/(3)}=(10^3)^{(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`

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Additional comments

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