Question

show that 5+√2 is an irrational​

Answer 1

let us assume that 5 + ✓2 is a rational number. then it can be represented in the a/b form.where a and B are coprime numbers and b is not equal to zero.

5+√2=a/b

=>√2=a-2b/b

as we know that root 2 is an irrational number. here √2 is equal to a-2b/b. so it contradicts our assumption.

hence 5+√2 is an irrational number.

hope you got it. please like the answer.....

Answer 2

$let \: us \: assume \: that \: 5 + \sqrt{2} \: is \: rational \: no \: . \\ \\ 5 + \sqrt{2} = \frac{p}{q} \\ \\ \sqrt{2} = \frac{p}{q} - 5 \\ \\ \frac{p}{q} - 5 \: is \: rational \: no. \\ \\ \sqrt{2} = irrational \: no \: . \\ \\ so \: by \: solving \: \frac{p}{q} - 5 \: we \: will \: get \: \: irrational \: no \: .$