How do you simplify #root(3)(3000)#?

Answer 1

You check to see if you can find a perfect cube to extract from the cube root.

Since #3000# is not a perfect cube itself, you're going to have to find a way of writing this number as a product between a perfect cube and another number.

In this case, you can write #3000# as being

#3000 = 1000 * 3 = 100 * 10 * 3 = 10 * 10 * 10 * 3 = 10""^3 * 3#

This means that the cube root can be simplified as

#root(3)(3000) = root(3)(10""^3 * 3)#

#root(3)(3000) = root(3)(10""^3) * root(3)(3) = color(green)(10 * root(3)(3))#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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