This week I had a bit of trouble with a couple of questions, including this one:

I had to arrange them in order. Since entire radicals are easier to organize than mixed radicals, I tried converting them. However, that did not go so well. I converted them by multiplying the coefficient by itself times ( = index). For example, on the first radical, . I got a ridiculously huge number, and since I was not allowed to use a calculator, I stopped multiplying after the 4th or 5th 7. I did the same for the remaining radicals, except for the last one which had me confused. As you can see, I received huge, huge numbers which aren’t very efficient for calculations…

After I ordered the first three radicals, I checked the answers, only to find that they were all incorrect. My strategy had worked in the past before, but for some reason I got the wrong answers with this conversion method.

I turned to my friend for help. She asked me what times itself 6 times equals 1, and I said 1. She then asked me to multiply 1 by 7, which is 7. And that’s the answer! Trying the same with the others, I converted them into simpler entire radicals without having to do complicated multiplication.

The last radical: 

——–>

, so !

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