In the 6th grade my math teacher showed the class a procedure to approximate square root. I asked whether there was a nice easy way to extract roots of higher powers. She said -- “No.” Few days later I came up to the teacher and asked her to raise any two-digit number to the third power and tell me the result. She obliged. Whereupon, it took me just a couple of seconds to tell her the original number she cubed. I asked to try it again with another number. She was annoyed, as there were no calculators back then, and raising a two-digit number into the third power was taking much longer than for me to take the root.

How is it done?

Can this trick be used with other powers? (Other than cube.)

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## Prime 15

In the 6th grade my math teacher showed the class a procedure to approximate square root. I asked whether there was a nice easy way to extract roots of higher powers. She said -- “No.” Few days later I came up to the teacher and asked her to raise any two-digit number to the third power and tell me the result. She obliged. Whereupon, it took me just a couple of seconds to tell her the original number she cubed. I asked to try it again with another number. She was annoyed, as there were no calculators back then, and raising a two-digit number into the third power was taking much longer than for me to take the root.

How is it done?

Can this trick be used with other powers? (Other than cube.)

Greater than 2-digit numbers?

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