how we know the cube root of 512 is 8

Question

anonymous · Answer

just see 8*8*8=512 or not if it is then cube root of 512 is 8

anonymous · Answer

how we know it is 8

anonymous · Answer

just factorise 512 with the help of 2's after factoring you will find 512=2^9 while 8=2^3
so 512=8^3

saifoo.khan · Answer

Prime factorization.

anonymous · Answer

devide 512 by it's prime factors (ie. numbers which can devide 512 and not yield fractions and which themselves have only 2 factors. these are 1,2,3, 5, 7, 11,13,17, etc you can pick out which ones work. and always use the lowest prime factor(LPF)

512=(2*256)     lpf=2
256=(2*128)      lpf=2
128=(2*64)
64=(2*32)
32=(2*16)
16=(2*8)
8=(2*4)
4=(2*2)
2=(2*1)

here the lowest prime factors are 2 everywher in the ladder

(Recall that $$8=2^{3}$$
so 512=2x2x2x2x2x2x2x2x2= (2x2x2)x(2x2x2)x(2x2x2)=8x8x8 . DONE!

Use the ladder method and find the LPF for each step