Question

write one example each of two irrational number whose
sum is ratinaol number difference is an irratinoal number​

Answer 1

$\huge\fbox{\tt{Question:-}}$

Write one example of each -

Two irrationals whose

• sum is rational number
• difference is an irrational number

$\huge\fbox{\tt{Answer:-}}$

Two irrationals whose sum is rational :

Irrational numbers :

• non terminating
• non recurring
• eg : √2 , √3 , √5

The two irrationals taken :

$\tt { (5+\sqrt{4}) (5-\sqrt{4})}$

Using the identity : (a+b)(a-b) = $\tt{ {a}^{2} - {b}^{2}}$

So , the value would be :

$\longrightarrow{\tt { {5}^{2} - {\sqrt{4}}^{2}}}$

$\longrightarrow{\tt { 25 - 4}}$

$\implies{\tt{21}}$

Note : 21 can be also written as $\tt{\frac{21}{1}}$

Two irrationals whose difference is irrational :

The two irrationals taken :

$\tt { (\sqrt{5}) - (\sqrt{2}) }$

So ,

$\longrightarrow{\tt{ \sqrt{5} - \sqrt{2}}}$

$\implies{\tt{\sqrt{3}}}$

$\tt{\sqrt{3} \:is \:an \:irrational\: number}$