Question

prove √3+√7 is an irrational ​

Answer 1

Step-by-step explanation:

let

root 3 + root 7 be a rational no

then

root 3 + root 7 =r

squaring both sides

(root 3 + root 7)^2 = (r)^2

(a+b)^2=a^2 +2ab+b^2

so

3 +2root 21 +7 = r^2

root 21=r^2-10/ 2

prove root 21 as irrational

RHS IS PURELY RATIONAL

LHS IS PURELY IRRATIONAL

SO IRRATIONAL AND RATIONAL CANNOT BE EQUAL

HENCE contradiction arises

therefore root 3 +root 7 is irrational

HOPE IT IS HELPFUL TO YOU

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