An example

An example is playfully for grade 6 from Math and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus:

A cuboid was made from a block of 16x18x48 mm of modeline. What will be the edge of the cube? If I calculate the cuboid volume, would I have to cube root or not? Thank you for your answer.

Correct result:

a2 =  24 mm


a=16 mm b=18 mm c=48 mm  V=a b c=16 18 48=13824 mm3 16=24 18=2 32 48=24 3  13824=29×33=(23)3 33=83 33=(8 3)3=243  V=a23 x0=a+b+c3=16+18+483=82327.3333 mm V0=273=19683 mm3 V1=283=21952 mm3 V3=263=17576 mm3 V4=253=15625 mm3 V5=243=13824 mm3 V5=V a2=24 mm   Verifying Solution:  13824=29 33=(23 3)3=(8 3)3=243 a2=24  a2=V3=138243=24 mm

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