Question

show that5+3√2 is an irrational number​

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

Let, 5 + 3√2 be a rational no. which can be written in the form of p/q where p and q are co-prime integers and q ≠ 0.

So,

$\implies \: 5 + 3 \sqrt{2} = \frac{p}{q}$

$\implies \: 3 \sqrt{2} = \frac{p}{q} - 5$

$\implies \: 3 \sqrt{2} = \frac{p \: - \: 5q}{q}$

$\implies \: \sqrt{2} = \frac{p \: - \: 5q}{3q}$

Now,

p/q is a rational number.

so, (p - 5q)/3q is also a rational number.

Therefore, √2 is also a rational number,

which contradicts our supposition that √2 is a rational number

Hence, √2 is an irrational number .

Therefore, 5 + 3√2 is also an irrational number.