Question

Show that
$( \sqrt{3 } + \sqrt{5} ) {}^{2}$
is an irrational number ​

Answer 1

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Let us assume that 3+5 is a rational number.

Now,

3+5=ba [Here a and b are co-prime numbers]

5=[(ba)−3]

5=[(ba−3b)]

Here, [(ba−3b)] is a rational number.

But we know that 5 is an irrational number.

So, [(ba−3b)] is also a irrational number.

So, our assumption is wrong.

3+5 is an irrational number.

Hence, proved.

$\huge\mathfrak\red{itz\:jyotsana☺}$

Answer 2

Answer:

i hope it will help you.