Question

Prove 3+4√5 is irrational Pls i neeed steps for this question

Answer 1

Answer:

Multiplication of rational and irrational number is irrational . So,4√5 is irrational. ... So,3+4√5 is irrational number....

Answer 2

Step-by-step explanation:

assume 3+4√5 as a rational number

now consider:

x=(√3+4√5)

squaring both the sides

x^2=(√3+4√5) whole square

x square=(√3) square+(4√5) square+2*√3*4√5

x square=3+80+8√15

x square=83+8√15

√15=83-x square/8

here x is a rational number

so, (83-x square/8) =√15

here √15 is a irrational number so (83-x square/8) is also irrational

this contraductory has arised due to our wrong assumption that (3+4√5) is a rational number.