Question

Prove that √8+5 is irrational​

Answer 1

Step-by-step explanation:

lets assume that

$\sqrt{8} + 5$

is a rational no.

therefore it can be represented in the p/q form where p and q are co-primes

$\sqrt{8} + 5 = \frac{x}{y} \\ \sqrt{8} = \frac{x - 5y}{y}$

here

$\sqrt{8} \: is \: not \: a \: rational \: no. \: but \: \frac{x - 5y}{y} \: is \: a \: rational \: no.$

therefore our assumption was wrong

therefore

$\sqrt{8} + 5 \: is \: an \: irrational \: no.$

Answer 2

Answer:

Step-by-step explanation:

let us assume root8+5is rational number

if root8+5 is rational it is in the form of p/q

q is not equal to zero where p and q are integers.

root8+5=a/b [where a and b are co-primes]

5/1-a/b=root8

5(b)-a(1)/b= root 8  [LCM]

5b-a/b=root8

in 5b-a/b ,a and b are integers so it is rational number

but this contradicts are fact that root 8 is irrational (root p is irrational )

there fore root 8+5 is irrational number

hence proved  

hope it is use full

thank you