Question

Show that:(3+√5) (3-√5) is a rational number

Answer 1

The value of
$(3 + \sqrt{5} )(3 - \sqrt{5} ) = 4$
We know that,

Rational numbers are those numbers which cam be expressed in the form of p /q where p and q are integers and q is not equal to 0

So,

4 is an integer of the form 4/1 i.e p/q where q=1

Thus,
4 is a rational number.


This means that

$(3 + \sqrt{5} )(3 - \sqrt{5} ) \: is \: also \: a \: rational \: number$

Thanks!

Answer 2

$3 {}^{2} - (\sqrt{5} ) {}^{2}$

$9 - 5$

$4 \: is \: your \: answer$