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:

The student made a cuboid from a block of 16x18x48 mm of plasticine. 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 answer:

a2 =  24 mm

Step-by-step explanation:

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=3a+b+c=316+18+48=38227.3333 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  mm  a2=3V=313824=24 mm



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