Question

√7+√3 is a rational no. Or irrational no.?explain

Answer 1

Hey there !!
____________________________________

√7 + √3 is an irrational number.

EXPLANATION :-

Let √ 7 + √3 be rational.

√7 + √3 = a / b
Squaring both sides

( √7 + √3 )² = ( a / b )²

10 + 2√21 = a² / b²

2√21 = ( a² / b² ) – 10

2√21 = ( a² – 10b² ) / b²

√21 = ( a² – 10b² ) / 2b²

Since a and b are integers, so ( a² – 10b² ) / 2b² is a rational number.
Thus, √21 is also a rational number.

But this contradicts the fact that √21 is an irrational number.
Our incorrect consumption is false.

So, we include that √7 + √3 is an irrational number.
____________________________________

Hope my ans.'s satisfactory. (^-^)