Start by decomposing the number inside the root into primes
Then group the terms into cubes if possible

rewrite the root
![\sqrt[3]{80}=\sqrt[3]{10\cdot2^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B80%7D%3D%5Csqrt%5B3%5D%7B10%5Ccdot2%5E3%7D)
then cancel the terms that are cubes and bring them out of the root
Let us start dividing 30 by small prime numbers in increasing order .
the smallest prime number we use is 2
Let's divide 30 by 2 quotient is 15
so we get : 30 = 2* 15
15 is not a prime number , it can be factorized further .
now we start dividing 15
2 can not divide 15 so we move to next prime number that is 3
can 3 divide 15? yes .
we get a quotient 5
so 30 is now : 2* 15 = 2* 3*5
now we have to work on 5 but 5 is a prime number so we stop here .
the prime factorization of 30 is : 2* 3* 5
Answer : 2 *3*5
Hmm
2 times 4=8
3 times 8 is not 27
1 times 1=1
2 times 4=8
3 times 9=27
aka
1 times 1^2=1
2 times 2^2=8
3 times 3^2=27
x times x^2=x^3
the rule is y=x^3
18÷19=0.94736....................