186,572 views
33 votes
33 votes
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...


User Sumith Ekanayake
by
3.2k points

2 Answers

17 votes
17 votes
Factor out the 2 so it’s radical 1000. Answer is 100
User Jakebrinkmann
by
2.1k points
10 votes
10 votes

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)

__

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

_____

Additional comments

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

User Mike Diaz
by
3.3k points