Can someone show me how this would turn out

  • Thread starter thomas49th
  • Start date
In summary, the conversation discusses determining the value and nature of the number \left(\frac{10}{3}\right)^{\frac{1}{2}} and whether it is rational or irrational. The speaker also asks for help in working out the problem and shares their thoughts on the irrationality of the number. The summary concludes that the number is irrational and cannot be accurately represented by a calculator due to its infinite decimal representation.
  • #1
thomas49th
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What would this number be?
[tex](3\frac{1}{3})^{\frac{1}{2}}[/tex]
Is it rational or irational?

How do you work it out?

[tex]\frac{10}{3}^\frac{1}{2}[/tex]
 
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  • #2
thomas49th said:
What would this number be?
[tex](3\frac{1}{3})^{\frac{1}{2}}[/tex]
Is it rational or irational?

How do you work it out?

[tex]\frac{10}{3}^\frac{1}{2}[/tex]

Your answer should be [tex]\left(\frac{10}{3}\right)^{\frac{1}{2}}[/tex]

Do you think it is rational or irrational?
 
  • #3
I THINK it's irrational, because it look ugly. Isn't it [tex]2\sqrt{\frac{10}{3}}[/tex]

As you put the denominator as the surd outside thingy (wot ever it's called) and the rest inside the root. On a calculator it gives me 2.108185... which is a real number, and virtually all real numbers are irrational?

P.S How do i tell on a calculator if the number is real or not. It could stop after 50 places, and my calculator only goes to 11
 
  • #4
You can't. ALL numbers a calculator deals with are rational and so, in general, only approximately the number you want.
 
  • #5
In general, if a rational number is not the ratio of two perfect squares, i.e. m2/n2, then its square root is not rational.
 

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