Question

Show that
$\sqrt{2 } + \frac{3}{ \sqrt{2} }$
ia a irrational number.

$class \: 10 \: \\ ch1 \: \: real \: number$
​

Answer 1

Solution :-

Let us assume that √2 + 3/√2 is an rational number

Therefore,

√2 + 3/√2 = a / b

[ a and b are coprime number where a and b ≠ 0

• Co prime numbers are those numbers which have only 1 as a common factor ]

By taking LCM

2 + 3 / √2 = a / b

5/√2 = a / b

5b/a = √2

Now, From above it is clear that √2 is rational

But it contradicts the fact that √2 is irrational

Hence, √2 + 3/√2 is irrational $.$