Question

Examine whether (√3+ 1/√3)^2 is rational or irrational

Answer 1

Answer:

yes, it is irrational no. because there is √3 and √3 is irrational.

Answer 2

Answer:

$(\sqrt{3} + \frac{1}{\sqrt{3} } )^{2}$

Using the property ( a + b )( a - b ) = $a^{2}$ + 2ab + $b^{2}$

$(\sqrt{3} + \frac{1}{\sqrt{3} } )^{2}$

I. √3

II. $\frac{1}{\sqrt{3} }$

Rationalize the denominator

Rationalizing factor = √3

$\frac{1}{\sqrt{3} }$  X $\frac{\sqrt{3} }{\sqrt{3} }$

$= \frac{\sqrt{3} }{3}$

$(\sqrt{3} + \frac{\sqrt{3} }{3} )^{2}$

$= (\sqrt{3} )^{2} + 2 X \sqrt{3} X \frac{\sqrt{3} }{3} + (\frac{\sqrt{3} }{3} )^{2}$

= 3 + 2 X $\frac{3}{3}$  + $\frac{3}{9}$

= 3 + 2 X 1 + $\frac{1}{3}$

= 3 + 2 + $\frac{1}{3}$

5 + $\frac{1}{3}$

$= \frac{15 + 1}{3}$

= $\frac{16}{3}$

= 5.3 bar

∴ It is a rational number beause it is a non-terminating recurring decimal.