Question

Prove that (√2+ √3)² is an irrational number.​

Answer 1

Step-by-step explanation:

(√2−√3)2(√2−√3)2

=(√2)2+(√3)2−2(√2∗√3)=(√2)2+(√3)2−2(√2∗√3)

=2+3+2√6=2+3+2√6

=5−2√6=5−2√6

Now,

2√6=√24=4.898979486(approx)2√6=√24=4.898979486(approx)

So,

(√2−√3)2(√2−√3)2

=5−2√6=5−2√6

=5−4.898979486=5−4.898979486

=0.101020514(approx)=0.101020514(approx)

N.B: The rule ab−−√=a−−√b√ab=ab does not always hold when we extend the √ function to complex numbers.