Question Video: ๐‘›th Roots: Integers Mathematics

Evaluate โˆœ16.


Video Transcript

Evaluate the fourth root of 16.

In order to answer this question, letโ€™s imagine that we say that the fourth root of 16 is equal to some root ๐‘Ÿ. In order to solve it then, we need to find this value of ๐‘Ÿ which when taken to the fourth power gives us 16. A really common mistake here would be to simply divide 16 by four and get an answer of four. However, weโ€™re not multiplying ๐‘Ÿ by four here, so we donโ€™t divide 16 by four. So letโ€™s see if we tried a value of one. One times one times one times one would simply give us one and not 16, so ๐‘Ÿ is not equal to one.

Next, letโ€™s try two. Well, two times two would give us four. Multiplying that by the next two would give us eight. And multiplying by the final two would give us 16. And therefore, that means that it must be two to the power of four, which equals 16. And since we worked out that this value of ๐‘Ÿ must be two, then that means that we can say that the fourth root of 16 is two.

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