Question

prove that 5+root2 is irrational ​

Answer 1

we know that root 2 is an irrational so multiple of root 2 also be irrational
and second method is this that you first find root 2 and then × 5 in your copy then you can prove that multiple of root 2 is an irrational number.

Hope it helped!

Answer 2

QUESTION:-

prove that 5+√2 is irrational™

SOLUTION:-

Let 5+√2= Rational

=>5+√2= $\frac{a}{b}$ [where a & b are co-prime integers they are not [equal to] irrational]

=>5+√2= $\frac{a}{b}$

=>√2=$\frac{a}{b}$-5

CROSS MULTIPLY RHS↓

√2=$\frac{a}{-5b}$

√2=$\frac{a}{-5b}$

=>LHS≠RHS[as Irrational≠Rational]

Creates a Contradiction Proving 5+√2 is IRRATIONAL✓

$\mathcal{BE \: BRAINLY}$