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Can someone show me how this would turn out

  • Thread starter thomas49th
  • Start date
655
0
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

cristo
Staff Emeritus
Science Advisor
8,056
72
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?
 
655
0
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
 
HallsofIvy
Science Advisor
Homework Helper
41,732
893
You can't. ALL numbers a calculator deals with are rational and so, in general, only approximately the number you want.
 
HallsofIvy
Science Advisor
Homework Helper
41,732
893
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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