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How do you find the cube roots #root3(8000)#?

Answer 1

Skylar Adams

#root3(8000)=root3((20⋅20⋅20)) = 20#

Find the cube roots #root3(8000#

Once you recognize that #root3(8# is #2#, then you will see how to factor #8000# into three perfect cubes.

#root3(8000) = root3(20*20*20)#

#root3(8000) = 20#

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Answer 2

Julian Avila

To find the cube root of 8000, you can use a calculator or manual calculation. Using a calculator, you can simply input "8000^(1/3)" or "8000^0.3333" to find the cube root, which is approximately equal to 20.

Manually, you can use the prime factorization method:

Find the prime factors of 8000:
( 8000 = 2^6 \times 5^3 )
Divide the powers of the prime factors by 3 (since we are finding the cube root):

( 2^{6/3} \times 5^{3/3} = 2^2 \times 5^1 = 4 \times 5 = 20 )

So, the cube root of 8000 is 20.

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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.