Can someone show me how this would turn out

  • Thread starter thomas49th
  • Start date
  • #1
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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]
 

Answers and Replies

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

Do you think it is rational or irrational?
 
  • #3
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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
HallsofIvy
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You can't. ALL numbers a calculator deals with are rational and so, in general, only approximately the number you want.
 
  • #5
HallsofIvy
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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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