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I don't think we need to memorize any bond length. However, we do need to understand how to calculate the average bond length based on the lewis structure(such as resonance structures) and the value of bond length given.
I also do not believe we will ever need to memorize different bond lengths. However, it's important to understand the trends behind bond lengths so that you can make predictions based on the information given. For example, triple bonds are shorter than single bonds. The bigger the atom, the larger the distance between it and its bonding atom; thus they have longer bonds. Longer bonds tend to be weaker, etc.
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