Math CentralQuandaries & Queries


Question from bobby, a parent:

what is the cubed root of 198

Hi Bobby,

You are looking for a number (I am going to call it a) so that a × a × a = a3 = 198. The best I can do is help you find an approximation to a. This is a calculator exercise. To start I need a first approximation (guess) and I know that 53 = 125 so what about 6? 63 = 216 which is too large so a is between 5 and 6.

My next approximation is 5.5 and 5.53 = 166.375 which is too small so a must be between 5.5 and 6.

Next I tried 5.8. 5.83 = 195.112 then 5.9, 5.93 = 205.375. We're getting close, a is between 5.8 and 5.9, probably closer to 5.8 then 5.9 so my next approximation might be 5.83.

When do you stop? That's up to you. When your approximation is accurate enough for your purposes you can stop.

I hope this helps,

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