Question

Show that 3root5 plus 5root3 is an irrationally number

Answer 1

In this given ex.
$3 \sqrt{5} + 5 \sqrt{3}$


is irrational number because we can't add root 5 and root 3
if the in root numbers are same then we aad its coefficient

Answer 2

Answer:

$3\sqrt{5}+5\sqrt{3}$ is irrational as sum of two irrational number is a irrational number.

Step-by-step explanation:

Given: 3root5 plus 5root3= $3\sqrt{5}+5\sqrt{3}$

To show : The given equation is irrational.

We know  $3\sqrt{5}$ and $5\sqrt{3}$ are the irrational numbers.

The sum of two irrational numbers will be irrational.

Except in some cases, where  the irrational parts of the numbers have a zero sum (cancel each other out), then the sum will be rational.

But in this case both the term are positive and not cancel each other.

Therefore,  $3\sqrt{5}+5\sqrt{3}$ is irrational as sum of two irrational number is a irrational number.