What is 5 root 2 Squared ?
- Thread starter shayodonn
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pka
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Please read the guidelines before posting.
Had you shown some of your own work it could have avoided some confusion.
As written, the question could be read \(\displaystyle (5\sqrt{2})^2\) OR \(\displaystyle 5(\sqrt2)^2\). Do you see the difference?
Which is it? Or is it something else altogether?
HallsofIvy
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"Five root 2" is terribly ambiguous. Most people, like pka, would interpret it as "5 times the square root of 2"- and even then "five root 2 squared" is ambiguous as to whether only "root 2" is being squared, \(\displaystyle 5(\sqrt{2})^2= 5(2)= 10\) or whether the whole "five root 2" is being squared, \(\displaystyle (5\sqrt{2})^2= 25(2)=50\).
I would go even further and worry that by "five root 2" you actually mean the fifth root of 2, \(\displaystyle \sqrt[5]{2}\). If that is what is meant, \(\displaystyle \left(\sqrt[5]{2}\right)^2\) can be written \(\displaystyle \sqrt[5]{2^2}= \sqrt[5]{4}\) or as \(\displaystyle 2^{\frac{2}{5}}= 4^{\frac{1}{5}}\).
I would go even further and worry that by "five root 2" you actually mean the fifth root of 2, \(\displaystyle \sqrt[5]{2}\). If that is what is meant, \(\displaystyle \left(\sqrt[5]{2}\right)^2\) can be written \(\displaystyle \sqrt[5]{2^2}= \sqrt[5]{4}\) or as \(\displaystyle 2^{\frac{2}{5}}= 4^{\frac{1}{5}}\).