Question

Show
that √6+√2
is
irrational​

Answer 1

Step-by-step explanation:

let us assume that √6+√2 is a rational number then,

√6+√2=a\b

√6=a/b-√2

squaring to both sides,

6=a2/b2+2-a/b√2

6-a2/b2-2=√2

4-a2/b2=√2

4a2-a2/b2=√2

this contradicts The fact that √2 is an irrational number

therefore our assumption is wrong and √6+√2 is an irrational number

Answer 2

Step-by-step explanation:

let us take √ 6 + √2 is a rational number

let us take two numbers a and b in which b is not equal to zero

rational number form is a/ b

√ 6 + √ 2 = a/ b

b × √ 6 + √ 2 = a

since a and b are integer where

b√ 6 √ + √ 2 are rational and a is also rational ..

this contradict the fact that b √ 6 + √ 2 is irrational hence our assumption is wrong ...

so √ 6+ √ 2 is irrational