Can someone show me how this would turn out

[thomas49th]

What would this number be?
$$(3\frac{1}{3})^{\frac{1}{2}}$$
Is it rational or irational?

How do you work it out?

$$\frac{10}{3}^\frac{1}{2}$$

 

[cristo]

What would this number be?
$$(3\frac{1}{3})^{\frac{1}{2}}$$
Is it rational or irational?

How do you work it out?

$$\frac{10}{3}^\frac{1}{2}$$

Your answer should be $$\left(\frac{10}{3}\right)^{\frac{1}{2}}$$

Do you think it is rational or irrational?

 

[thomas49th]

I THINK it's irrational, because it look ugly. Isn't it $$2\sqrt{\frac{10}{3}}$$

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]

You can't. ALL numbers a calculator deals with are rational and so, in general, only approximately the number you want.

 

[HallsofIvy]

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.